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IMOC 2017 G4 collinearity, orthocenter and circumcircle related

Source: https://artofproblemsolving.com/community/c6h1740077p11309077

March 20, 2020
geometrycircumcircleorthocentercollinear

Problem Statement

Given an acute △ABC\vartriangle ABC with orthocenter HH. Let MaM_a be the midpoint of BC.MaHBC. M_aH intersects the circumcircle of △ABC\vartriangle ABC at XaX_a and AXaAX_a intersects BCBC at YaY_a. Define Yb,YcY_b, Y_c in a similar way. Prove that Ya,Yb,YcY_a, Y_b,Y_c are collinear. https://2.bp.blogspot.com/-yjISBHtRa0s/XnSKTrhhczI/AAAAAAAALds/e_rvs9glp60L1DastlvT0pRFyP7GnJnCwCK4BGAYYCw/s320/imoc2017%2Bg4.png
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