Open ended Circle Problems

Open ended problems generate a variety of solutions and motivates the student to suggest different creative approaches in solving a problem. Here are two related to circle geometry.

Given a circle drawn on a piece of A4 paper. How can you find the diameter of the circle using only a ruler and a pencil?

Given pair of compass and straight edge, a circle and 2 points in the interior of the circle, inscribe a right-angled triangle in the circle such that the 2 points are on different sides of the triangle.