MathDB
Parallels and intouch triangle

Source: Kürschák 1993, problem 2

July 20, 2014
geometryprojective geometrygeometry unsolved

Problem Statement

Triangle ABCABC is not isosceles. The incircle of △ABC\triangle ABC touches the sides BCBC, CACA, ABAB in the points KK, LL, MM. The parallel with LMLM through BB meets KLKL at DD, the parallel with LMLM through CC meets KMKM at EE.
Prove that DEDE passes through the midpoint of LM‾\overline{LM}.
Back to ProblemsView on AoPS