MathDB
Mixtilinear Geometry

Source: KöMaL A. 817

March 23, 2022
geometrykomalmixtilinear incircle

Problem Statement

Let ABCABC be a triangle. Let TT be the point of tangency of the circumcircle of triangle ABCABC and the AA-mixtilinear incircle. The incircle of triangle ABCABC has center II and touches sides BC,CABC,CA and ABAB at points D,ED,E and F,F, respectively. Let NN be the midpoint of line segment DF.DF. Prove that the circumcircle of triangle BTN,BTN, line TITI and the perpendicular from DD to EFEF are concurrent.
Proposed by Diaconescu Tashi, Romania
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