MathDB
Bulgarian National Mathematical Olympiad 2016, Problem 5

Source:

June 22, 2017
geometrycircumcircle

Problem Statement

Let △ABC\triangle {ABC} be isosceles triangle with AC=BCAC=BC . The point DD lies on the extension of ACAC beyond CC and is that AC>CDAC>CD. The angular bisector of ∠BCD \angle BCD intersects BDBD at point NN and let MM be the midpoint of BDBD. The tangent at MM to the circumcircle of triangle AMDAMD intersects the side BCBC at point PP. Prove that points A,P,MA,P,M and NN lie on a circle.
Back to ProblemsView on AoPS