MathDB
EGMO 2015, Problem 1

Source:

April 16, 2015
geometryEGMOTriangletangentEGMO 2015

Problem Statement

Let ABC\triangle ABC be an acute-angled triangle, and let DD be the foot of the altitude from C.C. The angle bisector of ABC\angle ABC intersects CDCD at EE and meets the circumcircle ω\omega of triangle ADE\triangle ADE again at F.F. If ADF=45\angle ADF = 45^{\circ}, show that CFCF is tangent to ω.\omega .