MathDB
Hardcore geo

Source: Moldova TST 2019

March 8, 2019
geometryTST

Problem Statement

Quadrilateral ABCDABCD is inscribed in circle Γ\Gamma with center OO. Point II is the incenter of triangle ABCABC, and point JJ is the incenter of the triangle ABDABD. Line IJIJ intersects segments AD,AC,BD,BCAD, AC, BD, BC at points P,M,NP, M, N and, respectively QQ. The perpendicular from MM to line ACAC intersects the perpendicular from NN to line BDBD at point XX. The perpendicular from PP to line ADAD intersects the perpendicular from QQ to line BCBC at point YY. Prove that X,O,YX, O, Y are colinear.
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