Let △ABC be an acute triangle with orthocenter H. The circle Γ with center H and radius AH meets the lines AB and AC at the points E and F respectively. Let E′, F′ and H′ be the reflections of the points E, F and H with respect to the line BC, respectively. Prove that the points A, E′, F′ and H′ lie on a circle.Proposed by Jasna Ilieva geometrygeometric transformationreflection