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B,P,Q,R are collinear

Source: Indonesia National Science Olympiad D2 P4

September 5, 2012
geometrycircumcirclegeometry proposed

Problem Statement

Given a triangle ABCABC, let the bisector of ∠BAC\angle BAC meets the side BCBC and circumcircle of triangle ABCABC at DD and EE, respectively. Let MM and NN be the midpoints of BDBD and CECE, respectively. Circumcircle of triangle ABDABD meets ANAN at QQ. Circle passing through AA that is tangent to BCBC at DD meets line AMAM and side ACAC respectively at PP and RR. Show that the four points B,P,Q,RB,P,Q,R lie on the same line.
Proposer: Fajar Yuliawan
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