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AQ = BF wanted, touchpoints of incircle of right triangle ABC

Source: 2022 NZMO - New Zealand Maths Olympiad Round 2 p4

October 8, 2022
geometryincircleright triangle

Problem Statement

Triangle ABCABC is right-angled at BB and has incentre II. Points DD, EE and FF are the points where the incircle of the triangle touches the sides BCBC, ACAC and AB respectively. Lines CICI and EFEF intersect at point PP. Lines DPDP and ABAB intersect at point QQ. Prove that AQ=BFAQ = BF.
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