Given a triangle ABC inscribed in circle c(O,R) (with center O and radius R) with AB<AC<BC and let BD be a diameter of the circle c. The perpendicular bisector of BD intersects line AC at point M and line AB at point N. Line ND intersects the circle c at point T. Let S be the second intersection point of cicumcircles c1 of triangle OCM, and c2 of triangle OAD. Prove that lines AD,CT and OS pass through the same point.