A Parallelogram with Vertices on Two Circles

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.



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See problem 2666 in Crux Mathematicorum 28(7), 2002 pp. 462-3.
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