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Geometry Mathley 2.3 two lines and a circle concurrent

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June 6, 2020
geometryconcurrentorthocentercircumcircle

Problem Statement

Let ABCABC be a triagle inscribed in a circle (O)(O). A variable line through the orthocenter HH of the triangle meets the circle (O)(O) at two points P,QP , Q. Two lines through P,QP, Q that are perpendicular to AP,AQAP , AQ respectively meet BCBC at M,NM, N respectively. Prove that the line through PP perpendicular to OMOM and the line through QQ perpendicular to ONON meet each other at a point on the circle (O)(O).
Nguyễn Văn Linh
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