![]() ![]() Triangle ABC is a right triangle so using Pythagoras theorem x 2 + b 2 R 2 Substitute x h - R and solve for b. ![]() let b AB then b is half the length of the base of the isosceles triangle. The sides of the triangle are tangent to the circle. Since the triangle is isosceles A is the midpoint of the base. When a circle inscribes a triangle, the triangle is outside of the circle and the circle touches the sides of the triangle at one point on each side. Since the triangle is isosceles, the other angles are both 45. Not sure how to answer this question Any help will be appreciated. Drag any vertex to another location on the circle. Use Lagrange multipliers to show that, of all the triangles inscribed in a circle of radius R, the equilateral triangle has the largest perimeter. ![]() Misc 5 Find the maximum area of an isosceles triangle inscribed in the ellipse □^2/□^2 + □^2/□^2 = 1 with its vertex at one end of the major axis. For an obtuse triangle, the circumcenter is outside the triangle. As Doctor Rick said, there are several ways to have found these angles one is to use the fact that a central angle is twice the inscribed angle, so that for instance AOB 2ACB 90. The triangle of largest area inscribed in a circle is an equilateral triangle. ![]()
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