MathDB
Collinearity

Source: Turkey JBMO TST 2016 P4

May 22, 2016
geometrytrapezoidcollinearity

Problem Statement

In a trapezoid ABCDABCD with AB<CDAB<CD and AB∥CDAB \parallel CD, the diagonals intersect each other at EE. Let FF be the midpoint of the arc BCBC (not containing the point EE) of the circumcircle of the triangle EBCEBC. The lines EFEF and BCBC intersect at GG. The circumcircle of the triangle BFDBFD intersects the ray [DA[DA at HH such that A∈[HD]A \in [HD]. The circumcircle of the triangle AHBAHB intersects the lines ACAC and BDBD at MM and NN, respectively. BMBM intersects GHGH at PP, GNGN intersects ACAC at QQ. Prove that the points P,Q,DP, Q, D are collinear.
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