IMO 2022 Shortlist G3

Let ABCD be a cyclic quadrilateral. Assume that the points Q, A, B, P are collinear in this order, in such a way that th...

IMO 2022 Shortlist G3

Category: Geometry

Problem

Let ABCD be a cyclic quadrilateral. Assume that the points Q, A, B, P are collinear in this order, in such a way that the line AC is tangent to the circle ADQ, and the line BD is tangent to the circle BCP. Let M and N be the midpoints of BC and AD, respectively. Prove that the following three lines are concurrent: line CD, the tangent of circle ANQ at point A, and the tangent to circle BMP at point B. (Slovakia)