MathDB

2 lines intersect on circumcircle, orthocenter , reflections of line wrt lines

Source: Mathematics Regional Olympiad of Mexico Center Zone 2016 P3

November 12, 2021

geometryreflectionconcurrencyconcurrentorthocenter

Problem Statement

Let

ABC

be a triangle with orthocenter

H

and

\ell

a line that passes through

H

, and is parallel to

BC

. Let

m

and

n

be the reflections of

\ell

on the sides of

AB

and

AC

, respectively,

m

and

n

are intersect at

P

. If

HP

and

BC

intersect at

Q

, prove that the parallel to

AH

through

Q

and

AP

intersect at the circumcenter of the triangle

ABC