Source: Avital & Barbeau, "Intutively Misconceived Solutions to Problems," *For the Learning of Mathematics*, 1991

**Hint:** It is not equilateral....!

Use GSP to draw an isosceles triangle whose apex is the center of the circle and two radii form the equal sides. As you move a triangle vertex anchored on the circle, what happens to the area?

**Solution Commentary:** To overcome the first intuition of the answer being an equilateral triangle, the second intuition should be connected to other problems where you have maximal areas in polygons. Hint: Think square....and now can you prove your results?