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Just a symmedian problem

Source: 2023 Brazil Ibero TST P2

August 28, 2023
geometrysymmedian

Problem Statement

Let ABCDABCD be a parallelogram. The tangent to the circumcircle of triangle BCDBCD at CC intersects ABAB at PP and intersects ADAD at QQ. The tangents to the circumcircle of triangle APQAPQ at PP and QQ meet at RR. Show that points AA, CC, and RR are collinear.
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