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Fixed point

Source: Moscow Olympiad 2018, Grade 9, P4

July 13, 2018
geometrycircumcircle

Problem Statement

ABCDABCD is convex and AB∦CD,BC∦DAAB\not \parallel CD,BC \not \parallel DA. PP is variable point on ADAD. Circumcircles of △ABP\triangle ABP and △CDP\triangle CDP intersects at QQ. Prove, that all lines PQPQ goes through fixed point.
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