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Find The Angle!

Source: 2020 RMM Shortlist G1

October 8, 2022
geometryanglesRMMRMM 2020RMM Shortlist

Problem Statement

The incircle of a scalene triangle ABCABC touches the sides BC,CABC, CA, and ABAB at points D,ED, E, and FF, respectively. Triangles APEAPE and AQFAQF are constructed outside the triangle so that AP=PE,AQ=QF,∠APE=∠ACB, and ∠AQF=∠ABC.AP =PE, AQ=QF, \angle APE=\angle ACB,\text{ and }\angle AQF =\angle ABC.Let MM be the midpoint of BCBC. Find ∠QMP\angle QMP in terms of the angles of the triangle ABCABC.
Iran, Shayan Talaei
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