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Three concurrent lines in a triangle

Source: IMOC 2023 G2

September 9, 2023
geometry

Problem Statement

PP is a point inside △ABC\triangle ABC. AP,BP,CPAP, BP, CP intersects BC,CA,ABBC, CA, AB at D,E,FD, E, F, respectively. ADAD meets (ABC)(ABC) again at D1D_1. SS is a point on (ABC)(ABC). Lines ASAS, EFEF intersect at TT, lines TP,BCTP, BC intersect at KK, and KD1KD_1 meets (ABC)(ABC) again at XX. Prove that S,D,XS, D, X are colinear.
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