Let D be an arbitrary point on side AB of triangle ABC. Circumcircles of triangles BCD and ACD intersect sides AC and BC at points E and F, respectively. Perpendicular bisector of EF cuts AB at point M, and line perpendicular to AB at D at point N. Lines AB and EF intersect at point T, and the second point of intersection of circumcircle of triangle CMD and line TC is U. Prove that NC=NU geometrycircumcircleperpendicular bisector