Constructing Isosceles Triangles
Point A is the center of a circle, and points C and D are distinct, freely moving points on the circle. Explain why triangle ACD is isosceles.
Devise several other ways to construct an isosceles triangle. Explain how you know each of your solutions represents an isosceles triangle.

Extensions 
Repeat this exploration, but construct equilateral triangles.
Submit your idea for an investigation to InterMath.
