Problem

Source: Kazakhstan National Olympiad 2024 (10-11 grade), P1

Tags: geometry



Let ABC be an acute triangle with an altitude AD. Let H be the orthocenter of triangle ABC. The circle Ω passes through the points A and B, and touches the line AC. Let BE be the diameter of Ω. The lines~BH and AH intersect Ω for the second time at points K and L, respectively. The lines EK and AB intersect at the point~T. Prove that BDK=BLT.