Question 19
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 $ \angle PDC = \angle EDQ = \angle ADB $.
Prove that lines $ KP, LQ $, and MD are concurrent.
Prove that lines $ KP, LQ $, and MD are concurrent.