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Part of 2022 Cono Sur

Problems(1)

Equal segments in an incircle configuration

Source: Cono Sur 2022 #2

8/9/2022
Given is a triangle ABCABC with incircle ω\omega, tangent to BC,CA,ABBC, CA, AB at D,E,FD, E, F. The perpendicular from BB to BCBC meets EFEF at MM, and the perpendicular from CC to BCBC meets EFEF at NN. Let DMDM and DNDN meet ω\omega at PP and QQ. Prove that DP=DQDP=DQ.
geometrygeometry solvedincirclesimilar triangles