## Maximum Area Of A Triangle Inscribed In A Circle

The triangle formed by the diameter and the inscribed angle (triangle ABC above) is always a right triangle. units b) 1/2 r^2 sq. Occasionally it happens that for a given parabola the same value of `x` maximizes the area and the perimeter of the rectangle. Is there a way to limit a circle or something? Finding the maximum area of a rectangle with an inscribed triangle Calculating when two angles / objects will cross around a circle. The radius of the inscribed circle is called the inradius and equals S/σ. The problem is to maximize A = 4xy subject to the condition that x^2 + y^2 = R^2 (Note that R^2 is a constant) A = 4xy, so dA/dx = 4(x * dy/dx + y) Set this to 0. No matter where he places the third vertex, the following conditions will be true: • Each line will always bisect its corresponding vertex angle. Solution of exercise 6 The surface of a table consists of a square of 1 m per side and two semicircles attached on either opposite end. (see diagrams below) The triangle with angle θ can be bisected giving two right angled triangles with angles θ/2. The center of the incircle is a triangle center called the triangle's incenter. SOLUTION: Area of the largest triangle that can be inscribed in a semi-circle of radius r units is (A) r^2 sq. Find the Maximum Area of the Rectangle. A rectangle is inscribed in the triangle with one side on the triangle's base. So the central angle right over here is 180 degrees, and the inscribed angle is going to be half of that. So, the area of the rectangle is. Let Rbe the radius of the smallest circle containing all points in Son either the interior or boundary. Inequalities for the area of a triangle x9. The largest possible triangle that can be inscribed inside a semicircle is the right angled triangle whose hypotenuse is the diameter of the semicircle, and whose other two sides are equal. It is the four curved shapes at the four corners. 5/10/2019 1 Comment Inscribed Isosceles Kite Length Linear Function. The center of the incircle, ca. When t = 45 degrees, the area of the inscribed right triangle is maximum. So your initial rectangle inscribed into semicircle was [ r√2 ] x [ r/√2 ]. Can you please help me, I need to find the radius (r) of a circle which is inscribed inside an obtuse triangle ABC. 23 The area of a circle inscribed in an side 50 m 2 such that each can graze the maximum unshared area. I wasn't sure, and am still not, whether the circle was one that was outside and contained a roughly circular cluster of points, or whether there was a "hole" in the points (like a dotted donut) and he wanted the circle to be inside the points but containing the edge of the hole (essentially outlining the hole of the donut). Radius of a circle inscribed within a known triangle. This came from wondering if there was a way to quantify how circular a regular polygon was. There are two ways to do this: 1) With user interaction: Program will prompt user to enter the radius of the circle. Geometry Here is a list of all of the skills that cover geometry! These skills are organised by year, and you can move your mouse over any skill name to preview the skill. Express the area, A, within the circle, but outside the triangle, as a. The number of square units enclosed by the polygon is. The calculation for the radius of a square relies on the Pythagorean Theorem that describes the relationships of the sides of a right triangle: a2 + b2 = c2. and triangle is inscribed in the circle with center O and radius r. Let's focus first in the radius of each inscribed circle. Maximum area of a triangle inscribed in a circle radius R (optimization)? Best Answer: Yes, an equilateral triangle yields the largest area. When folded inwardly to the center they come together to produce the single shape that is the hypocycloid. Express the area, A, within the circle, but outside the triangle, as a. From the previous exercise you can see that the `x` value where the perimeter is maximized depends only on the parameter `a`. Maximum Area of Triangle. The center of the incircle is a triangle center called the triangle's incenter. An isosceles triangle is a triangle with two sides of the same length. Pythagorean Theorem. 7 hours ago. And what that does for us is it tells us that triangle ACB is a right triangle. The area of a segment in a circle is found by first calculating the area of the sector formed by the two radii and then subtracting the area of the triangle formed by the two radii and chord (or secant). When h = sqrt(2), w is the same length as h, so the inscribed rectangle which maximizes the area is a square. n Part B uses the same circle inscribed within a triangle in Part A to find the terms s-a, s-b, and s-c in the diagram. The length of sides AB and CB are given by AB = AC * cos (45 degrees) = 2 r sqrt(2) and CB = AC * sin (45 degrees) = 2 r sqrt(2). The properties are: 1. What is the maximum possible area of the triangle? 3. So the central angle right over here is 180 degrees, and the inscribed angle is going to be half of that. This is actually a nice problem for students to try, although not difficult. Find that area. Many resources like assessment examples, teaching notes, vocabulary lists, student worksheets, videos explanations, textbook connections, web links are all here to help teachers and students. u/ajmal1729. When a circle is inscribed within a square, the hypocycloid consists of all that area lying outside the circle but inside the square. The problem is to maximize A = 4xy subject to the condition that x^2 + y^2 = R^2 (Note that R^2 is a constant) A = 4xy, so dA/dx = 4(x * dy/dx + y) Set this to 0. Formulas for radius of circle inscribed in a triangle, square, trapezoid, regular hexagon, regular polygon, rhombus All formulas for radius of a circle inscribed - Calculator Online Home List of all formulas of the site. This page is the high school geometry common core curriculum support center for objective G. Isosceles Triangle Equations Formulas Calculator - Inscribed Circle Radius Geometry. The area of the remaining portion of the triangle is (\(\sqrt{3}\) =1. eNotes Home; the area of rectangle is maximum, A. There are two ways to do this: 1) With user interaction: Program will prompt user to enter the radius of the circle. (A) Area of the circle = Area of the square (B) Area of the circle > Area of the square (C) Area of the circle < Area of the square (D) Nothing definite can be said about the relation between the areas of the circle and square. Keywords:. A is (a, 0). The radius of the circle is the circum radius,R of the triangle. Maximum area of a triangle inscribed in a circle, ellipse, conic section [ 1 Answers ] A triangle inscribed in a circle has to be equilateral triangle for having maximum area ; how? What if it is an ellipse instead of a circle, or a conic section in general ?. To find the area of an equilateral triangle inscribed in a circle, the height of the triangle is $\frac32r$. the circum center of the circle will lie on the perpendicular from A to BC. We are asked to find this area, but we may also have to identify the rectangle which achieves this area along the way. Area Of Isosceles Triangle: Area Of Isosceles triangle is defined as the one upon two times. The ratio of the area of the inscribed square to the area of the large square is A) B) 5/9 C) 2/3 D) E) 7/9 13. Conversely, if one side of an inscribed triangle is a diameter, then the triangle is a right triangle, and the angle opposite the diameter is a right angle. Note that the result is derived for a unit circle for convenience. 12 Joshua is constructing a triangle with a circle inscribed in it. Find the area of the greatest rectangle that can be inscribed in an ellipse + =1. Express the area, A, within the circle, but outside the triangle, as a. an isolation triangle has a base of 6 units and a height of 12 units. Pull It All Together Let’s use a triangle with sides the length of 3, 4 and 5 as an example. The base of the triangle is 8 inches and the height is 10 inches. Learn more about maximal inscribed circle in fields of intersecting lines Image Processing Toolbox. Inequalities for the area of a triangle x9. Many resources like assessment examples, teaching notes, vocabulary lists, student worksheets, videos explanations, textbook connections, web links are all here to help teachers and students. What is the distance between the centers of those circles? Solution. Let variable x be the length of the base and variable y the height of the triangle, and consider angle. The ratio of the area of the inscribed square to the area of the large square is A) B) 5/9 C) 2/3 D) E) 7/9 13. n is the perimeter of the input triangle, or its area and radius of inscribed circle. The area of a segment in a circle is found by first calculating the area of the sector formed by the two radii and then subtracting the area of the triangle formed by the two radii and chord (or secant). units b) 1/2 r^2 sq. circumscribed circle and maximal inscribed circle. Thales Theorem states that any diameter of a circle subtends a right angle to any point on the circle. It is denoted with the letter s. What area will be left ungrazed ? has been inscribed. Find the rectangle of maximum area that can be inscribed in a right triangle? Rectangle inscribed within a circle, what is the dimensions of the rectangular area removed? More questions. Anil Kumar 2,480 views. Solution: We let the triangle be located so that its vertices are at — 0 ; 0 – , — 4 ; 0 – , and — 4 ; 3 –. Download the Solutions here. Visualization: You are given a semicircle of radius 1 ( see the picture on the left ). Following Archimedes' argument in The Measurement of a Circle (c. Relationship to Thales' Theorem. An equilateral triangle is inscribed in a circle of radius r, as shown below. If we place another triangle with the same height and base on top of this one, we get a. Correct answer Explanatory Answer Medium Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. Show that the triangle of maximum area thatcan be inscribed in a circle is an equilateral triangle. This problem can be tackled in many ways, some of which are more effective than others. Download the Activity Sheet here. Therefore, the area of AFB is smaller than that of ADB. Get an answer for 'Maximize the area of the rectangles inscribed the unit circle' and find homework help for other Math questions at eNotes. The formula to find the area of a triangle is A=1/2xbxh. Problem 23. Using the formula below, you can calculate the area of the quadrilateral. The golden ratio in an equilateral triangle. The incircle (inscribed circle) of a triangle is the largest circle contained in the triangle touching the three sides. The radii of the circumscribed, inscribed, and an escribed circle x6. Find the total surface area of an open cylindrical vessel of length 42 cm, and of external and internal diameters 20 cm and 6 cm respectively. Geometry calculator for solving the inscribed circle radius of a isosceles triangle given the length of sides a and b. Introduction Roundness measurements are used to evaluate and control the quality of cylindrical objects. So the central angle right over here is 180 degrees, and the inscribed angle is going to be half of that. A line segment inside a triangle is shorter than the longest side x11. Let the length and breadth of the rectangle inscribed in a. PROBLEM 1 : Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum. A triangle with sides of and has both an inscribed and a circumscribed circle. Here the basic thing is that. units b) 1/2 r^2 sq. Using the fact that , one of the most famous limits in calculus, it is easy to show that. asked by Georges on November 18, 2012; geometry. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. Area of Triangle = ½(Base × Height) Here is a triangle with a base of 5 cm and a height of 6 cm. Therefore, the area of AFB is smaller than that of ADB. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Thales Theorem states that any diameter of a circle subtends a right angle to any point on the circle. and triangle is inscribed in the circle with center O and radius r. Find the area inside the semi-circle which is not occupied by the triangle. For every inscribed circle (except the ones that are at 0, π / 2, and π) a right triangle, like the shown in Figure 4, can be created. Remark: A2 /4 in eq. Express the area in terms of h. Let variable x be the length of the base and variable y the height of the triangle, and consider angle. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. What area will be left ungrazed ? has been inscribed. b) Find the dimensions of the track that encloses the maximum rectangular area. Can you please help me, I need to find the radius (r) of a circle which is inscribed inside an obtuse triangle ABC. IXL will track your score, and the questions will automatically increase in difficulty as you improve!. 73 and π = 3. [Use √3 = 1. In other words, my area equation is a quadratic, and I'm supposed to find the maximum. The other two vertices of the rectangle are on the triangle's legs. where a,b,c,d are the side lengths, and p is half the perimeter: In the figure above, drag any vertex around the circle. If the area of the circle is not equal to that of the triangle, then it must be either greater or less. such that a circle can be inscribed in it touching all four sides, then a+c=b+d. Calculate the area of the right triangle with legs measuring 3 and 4 cm. A rectangle is inscribed in the triangle with one side on the triangle's base. Choice (4)Area of largest triangle inscribed in a rectangle is lw/2. Since the above area equation is a negative quadratic, then it graphs as an upside-down parabola, so the vertex is the maximum. Area of Triangle = ½(Base × Height) Here is a triangle with a base of 5 cm and a height of 6 cm. A Square Inscribed in a Circle. Express the area, A, within the circle, but outside the triangle, as a. Each face of a cube is painted either red or blue, each with probability. If one side of a triangle inscribed in a circle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. The center of the circumcircle of a triangle is where the side bisetors intersect. ⇒ Area of this circle = πr 2 = 154 (22/7) × r 2 = 154 ⇒ r 2 = 154 × (7/22) = 49 ∴ r = 7 cm Recall that incentre of a circle is the point of intersection of the angular bisectors. Click HERE to see a detailed solution to problem 15. In other words, my area equation is a quadratic, and I'm supposed to find the maximum. Maximum Area of Triangle. Remember to include units. Also the inscribed triangle is equilateral and thus each of its angles measures 60 degrees. Triangle ADB has the biggest area. (the circle touches all three sides of the triangle) I need to find r - the radius - which is starts on BC and goes up - up course the the radius creates two right angles on both sides of r. Find the maximum-area of an isosceles triangle inscribed in the ellipse with its vertex at one end of the major axis. Download the Solutions here. [Use √3 = 1. numbers of pipes or wires in a conduit. A is (a, 0). A circle is inscribed in a regular hexagon of side 2 3 cm. Geometry calculator for solving the inscribed circle radius of a isosceles triangle given the length of sides a and b. For example, if f n is the perimeter of the input triangle, S n is related to the minimum-weight triangulation problem also known as optimal triangulation in computational geometry. The calculation for the radius of a square relies on the Pythagorean Theorem that describes the relationships of the sides of a right triangle: a2 + b2 = c2. units d)square root(2) r2 sq. 13 about constructing geometric inscribed polygons. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. In order to find this diagonal, which is the hypotenuse in a 45-45-90 triangle,. Here the basic thing is that. One last triangle area formula is: ½bcsin A, where b and c are two sides and angle A is the angle between them. In the ²gure above a square is inscribed in a circle If the area of the circle from GMAT 101 at California State University, Chico. 23 The area of a circle inscribed in an side 50 m 2 such that each can graze the maximum unshared area. It accepts scientific notation and converts immediately. what would be the radius of a circle that can be inscribed in a triangle with sides of 35, 29 and 64?. Another method of finding the area of a triangle can be applied, again, if the vertices are lattice points. Perimeter Examples Answer the following. Find the rectangle of maximum area that can be inscribed in a right triangle? Rectangle inscribed within a circle, what is the dimensions of the rectangular area removed? More questions. PROBLEM 16 : What angle between two edges of length 3 will result in an isosceles triangle with the largest area ?. Let Rbe the radius of the smallest circle containing all points in Son either the interior or boundary. When t = 45 degrees, the area of the inscribed right triangle is maximum. The semiperimeter of a triangle equals half the sum of its sides. Show that the triangle of maximum area thatcan be inscribed in a circle is an equilateral triangle. Remember to include units. 784 One could start by saying that the isosceles triangle with largest area inscribed in a triangle is also an equilateral triangle. For every inscribed circle (except the ones that are at 0, π / 2, and π) a right triangle, like the shown in Figure 4, can be created. 707 (since sin 45 ° = 0. A is (a, 0). 707) Area = ½ × 24. of the triangle, which is alse the radius of the circle is r = Sqrt[2^2 + 1^2] =Sqrt[5] Therefore, the area of the semicircle is. units (B) 1 2. In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. So the area is going to be equal to the square root of s, which is 3a over 2, times s minus a. Remember this tool should be used only to calculate area, perimeter or volume of a figure. In other words, my area equation is a quadratic, and I'm supposed to find the maximum. So that's 3a over 2 minus a. Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area. What is the area of a 45-45-90 triangle, with a hypotenuse of 8mm in length? What is the perimeter of an isosceles triangle whose base is 16 cm and whose height is 15 cm? The length of the base of an isosceles triangle is 4 inches less than the length of one of the two. 23 The area of a circle inscribed in an side 50 m 2 such that each can graze the maximum unshared area. Find an answer to your question Circle C is inscribed in triangle JEG. Choice (4)Area of largest triangle inscribed in a rectangle is lw/2. Consider radius CD of this circle perpendicular to AB. The area A is at a maximum when x = 1/√2. o get the max area for triangle, the circum centre of the triangle has to be the centre of the circle. The longer side subtends the greater angle x10. For a unit square given in the question, the radius is $\frac 12$ and the corresponding maximum area is, $$[AIE]_{max} = \frac 14$$. The intersection of the angle bisectors of an isosceles triangle is the center of an inscribed circle which is point O. PROBLEM 16 : What angle between two edges of length 3 will result in an isosceles triangle with the largest area ?. For example, start at the north pole. It accepts scientific notation and converts immediately. n Part A inscribes a circle within a triangle to get a relationship between the triangle's area and semiperimeter. We need to find variables in which it is easy to write the constraint and the formula for the triangle's area. If the triangle is very small (compared to the size of the sphere), the effects of curvature are negligible. Inequalities for the area of a triangle x9. The radius of the circle is the circum radius,R of the triangle. Note that the result is derived for a unit circle for convenience. This is actually a nice problem for students to try, although not difficult. In other words, my area equation is a quadratic, and I'm supposed to find the maximum. a) 98 cm*cm b)196 cm*cm c)392 cm*cm d)142. Each vertex of the triangle will have a line passing through it bisecting the angle. When t = 45 degrees, the area of the inscribed right triangle is maximum. Problems start middle-AMC level and go all the way to early IMO Shortlist level. If the area of the circle is not equal to that of the triangle, then it must be either greater or less. Its height EF is shorter than CD because EF is a leg and CF that equals CD is the hypotenuse of CEF. If one inscribes a circle in an ideal hyperbolic triangle, its points of tangency form an equilateral triangle with side length 4 ln phi! One can then place horocycles centered on the ideal triangle's vertices and tangent to each side of the inner equilateral triangle. The triangle is the largest when the perpendicular height shown in grey is the same size as r. units d)square root(2) r2 sq. Find the rectangle of maximum area that can be inscribed in a right triangle? Rectangle inscribed within a circle, what is the dimensions of the rectangular area removed? More questions. This formula is related to the cross. Geometry Here is a list of all of the skills that cover geometry! These skills are organised by year, and you can move your mouse over any skill name to preview the skill. So, use the side length rules for a 45-45-90 triangle. given: ABC is an isosceles triangle such that AB=AC. 2, Find the area of the inscribed circle. The center of the incircle, ca. b) Find the dimensions of the track that encloses the maximum rectangular area. To calculate the area of a segment bounded by a chord and arc subtended by an angle θ , first work out the area of the triangle, then subtract this from the area of the sector, giving the area of the segment. This is a particular case of Thales Theorem, which applies to an entire circle, not just a semicircle. This formula is related to the cross. A rectangle of maximum area is inscribed in the circle z 3 4i 1 If one vertex from ORGANIZATI 87500 at Sarhad University of Science and Information Technology, Peshawar. For example, if f n is the perimeter of the input triangle, S n is related to the minimum-weight triangulation problem also known as optimal triangulation in computational geometry. Since the circle has radius 3, |QC| = 3. For every inscribed circle (except the ones that are at 0, π / 2, and π) a right triangle, like the shown in Figure 4, can be created. The center of the circumcircle of a triangle is where the side bisetors intersect. There is no loss of generality in considering the case of a semicircle with unit radius. Let APQ be the isosceles triangle inscribed in the ellipse with centre at C. Since the base sits on the diameter of the semicircle, the height is r,. Methods used for determining the roundness are the least-squares circle (LSC), maximum inscribed circle (MIC), minimal. It accepts scientific notation and converts immediately. We seek to minimize the area of the triangle subject to the constraint that it is inscribed in the circle. (We say that the sphere is locally flat. Anil Kumar 2,480 views. Problem In the figure below, triangle ABC is a triangle inscribed inside the circle of center O and radius r = 10 cm. Trig Calculus -- Maximum Area of Isosceles Triangle Inscribed in a Circle - Duration: 16:39. Using Figure A, since angles 2 and 3 are inscribed angles Secondly, we note that angle 1, formed at the intersection of the two chords AB and CD, is an exterior angle with respect to angles 2 and 3 in triangle ACQ. Let the length and breadth of the rectangle inscribed in a. Choice (4)Area of largest triangle inscribed in a rectangle is lw/2. Let APQ be the isosceles triangle inscribed in the ellipse with centre at C. The radius of the circle is the circum radius,R of the triangle. An inscribed circle is the largest possible circle that can be drawn on the inside of a plane figure. ) Therefore in our equilateral triangle, the interior angles are 60 degrees. The golden ratio in an equilateral triangle. Now, let's take a closer look to this triangle. 5/10/2019 1 Comment Inscribed Isosceles Kite Length Linear Function. shaded region. There are a couple different ways of finding the vertex. 65) A formula for the area of a triangle is: Where s is the semi-perimeter (half perimeter) and a, b, c are side lengths. Isosceles Triangle Equations Formulas Calculator - Inscribed Circle Radius Geometry. Describe all parabolas that have an inscribed rectangle of maximum perimeter at `x = 1`. Relationship to Thales' Theorem. Area of Inscribed Triangle) Dear Shawn, Here is help with a solution to finding angles of a triangle having maximum area if it is drawn within a circle so that the triangle's vertices just touch the circle's perimeter (i. (Note: since BC is the >diameter of the circle, angle A = 900 degrees Wow, I think you mean angle A = 90 degrees. We are asked to find this area, but we may also have to identify the rectangle which achieves this area along the way. Sin(θ/2) = a/R. Geometry calculator for solving the inscribed circle radius of an equilateral triangle given the length of a side Equilateral Triangle Equations Formulas Calculator - Inscribed Circle Radius Geometry AJ Design. Problem 23. Find the perimeter of a square with side length 5 in. The results we provide are accurate, but rounded to the 12th decimal place. (3) 2002-WO8-3. There is no loss of generality in considering the case of a semicircle with unit radius. Then P has parallel tangents at a and c with slope m , where m = - m ac. Once you have all the information needed, you can find the total area of a triangle. Maximize the area of the right triangles inscribed in the unit semicircle. a rectangle is inscribed such that it has maximum area. Consider radius CD of this circle perpendicular to AB. The area of this polygon is n times the area of triangle, since n triangles make up this polygon. a) 98 cm*cm b)196 cm*cm c)392 cm*cm d)142. From point O, draw a line which is perpendicular to AB, draw a line which is perpendicular to AC, and draw a line which is perpendicular to BC. A Square Inscribed in a Circle. The three lines connecting a vertex and the opposite touchpoint of the incircle intersect in the Gergonne point. Inscribed right triangle problem with detailed solution. o get the max area for triangle, the circum centre of the triangle has to be the centre of the circle. The area of the remaining portion of the triangle is (\(\sqrt{3}\) =1. If the area of the circle is not equal to that of the triangle, then it must be either greater or less. 784 One could start by saying that the isosceles triangle with largest area inscribed in a triangle is also an equilateral triangle. It is easily demonstrated that a triangle inscribed in a semicircle is a Right Triangle. Relationship to Thales' Theorem. Keywords: circumscribed, inscribed, circle, Voronoi, roundness. Conversely, if one side of an inscribed triangle is a diameter, then the triangle is a right triangle, and the angle opposite the diameter is a right angle. Pull It All Together Let’s use a triangle with sides the length of 3, 4 and 5 as an example. Let the inscribed rectangle have sides 2x and 2y. Video by Art of Problem Solving's Richard Rusczyk, a MATHCOUNTS alum. If one inscribes a circle in an ideal hyperbolic triangle, its points of tangency form an equilateral triangle with side length 4 ln phi! One can then place horocycles centered on the ideal triangle's vertices and tangent to each side of the inner equilateral triangle. Solution: We let the triangle be located so that its vertices are at — 0 ; 0 – , — 4 ; 0 – , and — 4 ; 3 –. Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 4? Section 3. For the inscribed circle of a triangle, you need only two angle bisectors; their intersection will be the center of the circle. Geometry Here is a list of all of the skills that cover geometry! These skills are organised by year, and you can move your mouse over any skill name to preview the skill. Inscribed Solids. Find an answer to your question Circle C is inscribed in triangle JEG. Inequalities for the area of a triangle x9. Step 1: Note that maximizing the area of the ellipse is equivalent to maximizing area( 𝑙𝑙𝑖𝑝 ) area( 𝑖 𝑛 𝑙 ) Because the triangle is fixed. When a circle is inscribed within a square, the hypocycloid consists of all that area lying outside the circle but inside the square. 7 Update: This is problem # 26 of Larson Calculus (8th edition) or # 24 of the sixth edition. Calculate the area of a circular sector whose chord is the side of an inscribed equilateral triangle in a circle with a 2 cm radius. When folded inwardly to the center they come together to produce the single shape that is the hypocycloid. Let the radius of the circle be R. ? Maximize the area of the iscosceles triangles inscribe in the unit circle? More questions. Trig Calculus -- Maximum Area of Isosceles Triangle Inscribed in a Circle - Duration: 16:39.