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PC_|_AK wanted, 2 touchpoints of incircle related

Source: 2015 Baltic Way Shortlist G8 BW https://artofproblemsolving.com/community/c2641329_baltic_way_shortlist__geometry

November 23, 2021
geometryperpendicularincircle

Problem Statement

Let ABCABC be a scalene triangle. Let DD and EE be the points where the incircle touches sides BCBC and CACA, respectively. Let KK be the common point of line BCBC and the bisector of the angle ∠BAC\angle BAC. Let ADAD intersect EKEK in PP. Prove that PCPC is perpendicular to AKAK.
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