Altitudes AH1 and BH2 of acute triangle ABC intersect at H. Let w1 be the circle that goes through H2 and touches the line BC at H1, and let w2 be the circle that goes through H1 and touches the line AC at H2. Prove, that the intersection point of two other tangent lines BX and AY( X and Y are different from H1 and H2) to circles w1 and w2 respectively, lies on the circumcircle of triangle HXY.
Proposed by Danilo Khilko geometrycircumcircleTangent LineAngle Chasingtrigonometrygeometry unsolved