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JBMO Shortlist 2021 G5

Source: JBMO Shortlist 2021

July 2, 2022
JuniorBalkanshortlist2021geometryAngle Chasing

Problem Statement

Let ABCABC be an acute scalene triangle with circumcircle ω\omega. Let PP and QQ be interior points of the sides ABAB and ACAC, respectively, such that PQPQ is parallel to BCBC. Let LL be a point on ω\omega such that ALAL is parallel to BCBC. The segments BQBQ and CPCP intersect at SS. The line LSLS intersects ω\omega at KK. Prove that ∠BKP=∠CKQ\angle BKP = \angle CKQ.
Proposed by Ervin Macić, Bosnia and Herzegovina
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