MathDB
Lots of circles and lines

Source: Bosnia and Herzegovina TST 2015 day 1 problem 2

May 16, 2015
geometrycircumcircleperpendicular bisector

Problem Statement

Let DD be an arbitrary point on side ABAB of triangle ABCABC. Circumcircles of triangles BCDBCD and ACDACD intersect sides ACAC and BCBC at points EE and FF, respectively. Perpendicular bisector of EFEF cuts ABAB at point MM, and line perpendicular to ABAB at DD at point NN. Lines ABAB and EFEF intersect at point TT, and the second point of intersection of circumcircle of triangle CMDCMD and line TCTC is UU. Prove that NC=NUNC=NU