A Parallelogram with Vertices on Two Circles

vertical position of O

radius of first circle (gold)

radius of second circle (green)

rotate M

Let a circle have diameter AB and let M be a point on another circle with center at A. Let the circles intersect at C and D. Let BM, CM, and DM intersect the first circle at N, P, and Q, respectively. Then MPBQ is a parallelogram.