MathDB

14

Part of 2015 Baltic Way

Problems(1)

Concurrency. Geometry

Source: Baltic Way 2015

11/8/2015
In the non-isosceles triangle ABCABC an altitude from AA meets side BCBC in DD . Let MM be the midpoint of BCBC and let NN be the reflection of MM in DD . The circumcirle of triangle AMNAMN intersects the side ABAB in P≠AP\ne A and the side ACAC in Q≠AQ\ne A . Prove that AN,BQAN,BQ and CPCP are concurrent.
geometrygeometric transformationreflectioncircumcircle