Question

The only way to circumscribe a circle around a parallelogram is to make the parallelogram a what?

Answer 1

A parallelogram that can have a circle circumscribed around it must be a rectangle.

Explanation:

Here's how that is so. Let `ABCD` be the parallelogram. Opposire sides `AB` and `CD` are congruent chords of the circle, so arcs `AB` and `CD` are congruent. Add `BC` to both arcs and conclude that arcs `ABC` and `BCD` are congruent. Then chords `AC` and `BD` which are diagonals of the parallelogram are congruent, and the diagonals of a parallelogram are congruent only if it's a rectangle.