IMO 2020 Shortlist G5

Let ABCD be a cyclic quadrilateral with no two sides parallel. Let K, L, M, and N be points lying on sides AB, BC, CD, a...

IMO 2020 Shortlist G5

Category: Geometry

Problem

Let ABCD be a cyclic quadrilateral with no two sides parallel. Let K, L, M, and N be points lying on sides AB, BC, CD, and DA, respectively, such that KLMN is a rhombus with KL k AC and LM k BD. Let ω1, ω2, ω3, and ω4 be the incircles of triangles ANK, BKL, CLM, and DMN, respectively. Prove that the internal common tangents to ω1 and ω3 and the internal common tangents to ω2 and ω4 are concurrent. (Poland)