MathDB

G1

Part of 2020 Romanian Master of Mathematics Shortlist

Problems(1)

Find The Angle!

Source: 2020 RMM Shortlist G1

10/8/2022
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
geometryanglesRMMRMM 2020RMM Shortlist