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Easy Geometry, Colinear Points

Source: 2015 Korean Junior MO P1

November 1, 2015
geometrycircumcircle

Problem Statement

In an acute, scalene triangle △ABC\triangle ABC, let OO be the circumcenter. Let MM be the midpoint of ACAC. Let the perpendicular from AA to BCBC be DD. Let the circumcircle of △OAM\triangle OAM hit DMDM at P(≠M)P(\not= M). Prove that B,O,PB, O, P are colinear.
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