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computational geo with 2 circles

Source: III Soros Olympiad 1996-97 R3 9.4 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 31, 2024
geometry

Problem Statement

A chord AB=aAB = a is drawn in a circle of radius BB. A circle with center on line ABAB passes through AA and intersects this circle a second time at point CC. Let MM be an arbitrary point of the second circle. Straight lines MAMA and MCMC intersect the first circle a second time at points PP and QQ. Find PQPQ.
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