Quadrilateral ABCD is inscribed in a circle. Let ωA, ωB, ωC, ωD be the incircles of triangles DAB, ABC, BCD, CDA respectively. The common external common tangent of ωA, ωB, different from line AB, meets the external common tangent of ωA, ωD, different from AD, at point A′. Similarly, the external common tangent of ωB, ωC different from BC meets the external common tangent of ωC, ωD different from CD at C′.
Prove that AA′∥CC′. geometrycyclic quadrilateralincirclesnational olympiad