MathDB

2.3

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 2.3 two lines and a circle concurrent

Source:

6/6/2020
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
geometryconcurrentorthocentercircumcircle