Given a circle (O, R) with diameter AB. Point M on (O), A, B are not coincident. Two lines through O and perpendicular to AM, BM intersects the tangent of (O) through M at C, D, respectively. OC intersects AM at I, OD intersects BM at K. Prove that IK, AD, BC are concurrent.
Attempts: I tried drawing an altitude through M of triangle ABC, intersecting IK at some point but still stuck on proving that it is the midpoint of that altitude. AC, BD are tangents of (O) and I, K are midpoints of AM, BM respectively has been proved.