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IMOC 2018 G3 (CY is tangent to circumcircle of BCC', orthocenter related)

Source: https://artofproblemsolving.com/community/c6h1740825p11314688

March 22, 2020
geometrytangentcircumcircleorthocenter

Problem Statement

Given an acute △ABC\vartriangle ABC whose orthocenter is denoted by HH. A line ℓ\ell passes HH and intersects AB,ACAB,AC at P,QP ,Q such that HH is the mid-point of P,QP,Q. Assume the other intersection of the circumcircle of △ABC\vartriangle ABC with the circumcircle of △APQ\vartriangle APQ is XX. Let C′C' is the symmetric point of CC with respect to XX and YY is the another intersection of the circumcircle of △ABC\vartriangle ABC and AOAO, where O is the circumcenter of △APQ\vartriangle APQ. Show that CYCY is tangent to circumcircle of △BCC′\vartriangle BCC'. https://1.bp.blogspot.com/-itG6m1ipAfE/XndLDUtSf7I/AAAAAAAALfc/iZahX6yNItItRSXkDYNofR5hKApyFH84gCK4BGAYYCw/s1600/2018%2Bimoc%2Bg3.png
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