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Line bisects segment

Source: Tuymaada 2018 Senior League/Problem 3

July 20, 2018
circumcircleTrianglegeometry

Problem Statement

A point PP on the side ABAB of a triangle ABCABC and points SS and TT on the sides ACAC and BCBC are such that AP=ASAP=AS and BP=BTBP=BT. The circumcircle of PSTPST meets the sides ABAB and BCBC again at QQ and RR, respectively. The lines PSPS and QRQR meet at LL. Prove that the line CLCL bisects the segment PQPQ.
Proposed by A. Antropov
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