IMO 2024 Shortlist G3
Let ABCDE be a convex pentagon and let M be the midpoint of AB. Suppose that segment AB is tangent to the circumcircle o...
Category: Geometry
Problem
Let ABCDE be a convex pentagon and let M be the midpoint of AB. Suppose that segment AB is tangent to the circumcircle of triangle CME at M and that D lies on the circumcircles of triangles AME and BMC. Lines AD and ME intersect at K, and lines BD and MC intersect at L. Points P and Q lie on line EC so that =PDC “ =EDQ “ =ADB. Prove that lines KP, LQ, and MD are concurrent. (Belarus)