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Incircle geometry with locus

Source: Caucasus MO 2024, Seniors P8

March 13, 2024
geometry

Problem Statement

Let ABCABC be an acute triangle and let XX be a variable point on ACAC. The incircle of △ABX\triangle ABX touches AX,BXAX, BX at K,PK, P, respectively. The incircle of △BCX\triangle BCX touches CX,BXCX, BX at L,QL, Q, respectively. Find the locus of KP∩LQKP \cap LQ.
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