Optimized Circle Inscribed in an Isosceles Triangles

Author:
DNghiem
Optimization Problem: A circle is inscribed in an isosceles triangle (the two equal sides have length one). Use Calculus (and some trigonometry!) to find the length of the third side of the triangle that allows that largest circle to be inscribed. Directions: You may click and drag Points A, B, and C to see how the Area of the circle varies as the Base changes.
1.) By experimenting with differing bases, can you find the one that maximizes Area? 2.) Use Calculus to verify your answer.