Let ω be a circle and let A be a point lying outside of ω. The tangents from A to ω touch ω at points B and C. Let M be the midpoint of BC and let D a point on the side BC different from M. The circle with diameter AD intersects ω at points X and Y and the circumcircle of △ABC again at E. Prove that AD, EM, and XY are concurrent. TSTgeometrycircleChordsconcurrent linesTangents