Another Catriona Shearer puzzle.

**11.
All in the Square**

Spoiler!

This is cute. Never mind the big diagram, just consider a circle inscribed in a right triangle with hypotenuse :

With the vertices and contact points joined to the incenter, you can see the triangle is divided into an square and four triangles, two of which can be rearranged: to make an rectangle. So the triangle’s area equals . Solving, and with , , we get ; the circle’s area is .