Let A1 and C1 be the tangency points of the incircle of triangle ABC with BC and AB respectively, A′ and C′ be the tangency points of the excircle inscribed into the angle B with the extensions of BC and AB respectively. Prove that the orthocenter H of triangle ABC lies on A1C1 if and only if the lines A′C1 and BA are orthogonal. geometryratioincentercircumcircletrigonometrygeometry proposed