Problem

Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 8.6

Tags: geometry, cyclic quadrilateral



Cyclic quadrilateral $ABCD$ is such that $\angle BAD = 2\angle ADC$ and $CD = 2BC$. Let $H$ be the projection of $C$ onto $AD$. Prove that $BH \parallel CD$. Proposed by Fedir Yudin, Anton Trygub