Problem

Source: Kyiv City MO 2025 Round 1, Problem 9.3

Tags: geometry, tangent



Point H is the orthocenter of the acute triangle ABC, and AD is its altitude. Tangents are drawn from points B and C to the circle with center A and radius AD, which do not coincide with the line BC. These tangents intersect at point P. Prove that the radius of the incircle of BCP is equal to HD. Proposed by Danylo Khilko