Question

2. Given a circle and a rectangle, what must be true about the rectangle for it to be possible to inscribe a congruent copy of it in the circle?

Answer 1

The diagonal of the rectangle must be equal to the diameter of the circle.

Explanation:

The point where the diagonals of a rectangle cross will be the center of a circumscribing circle. Obviously, the vertices of the rectangle lie on the circle, so either diagonal will be a diameter of the circle.

In order for it to be possible to inscribe a rectangle in a circle, its diagonal measure must match the diameter of the circle.