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2013 ToT Spring Junior A p6 peprendicular wanted and given, incircle

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March 4, 2020
perpendicularincirclegeometry

Problem Statement

Let ABCABC be a right-angled triangle, II its incenter and B0,A0B_0, A_0 points of tangency of the incircle with the legs ACAC and BCBC respectively. Let the perpendicular dropped to AIAI from A0A_0 and the perpendicular dropped to BIBI from B0B_0 meet at point PP. Prove that the lines CPCP and ABAB are perpendicular.
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