Problem

Source: V.A. Yasinsky Geometry Olympiad 2023 IX p6, Ukraine

Tags: geometry, Equilateral



An acute triangle $ABC$ is surrounded by equilateral triangles $KLM$ and $PQR$ such that its vertices lie on the sides of these equilateral triangle as shown on the picture. Lines $PK$ and $QL$ intersect at point $D$. Prove that $\angle ABC + \angle PDQ = 120^o$. (Yurii Biletskyi)