A. 591. There is given a convex quadrilateral ABCD and some points P, Q, R and S on the line segments AB, BC, CD and DA, respectively. The line segments PR and QS meet at T. Suppose that each of the the quadrilaterals APTS, BQTP, CRTQ and DSTR have an inscribed circle. Prove that the quadrilateral ABCD also has an inscribed circle.
Solution (in Hungarian)