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Tangent Length Inside the Incircle

Source: KMO 2022 P5

October 29, 2022
geometryincenter

Problem Statement

For a scalene triangle ABCABC with an incenter II, let its incircle meets the sides BC,CA,ABBC, CA, AB at D,E,FD, E, F, respectively. Denote by PP the intersection of the lines AIAI and DFDF, and QQ the intersection of the lines BIBI and EFEF. Prove that PQ‾=CD‾\overline{PQ}=\overline{CD}.
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