MathDB

concurrency wanted, reflections of feet of altitudes, orthocenter

Source: 2019 Balkan MO Shortlist G7 - BMO

November 19, 2020

geometryreflectionconcurrencyconcurrentorthocenter

Problem Statement

Let

AD, BE

, and

CF

denote the altitudes of triangle

\vartriangle ABC

. Points

E'

and

F'

are the reflections of

E

and

F

over

AD

, respectively. The lines

BF'

and

CE'

intersect at

X

, while the lines

BE'

and

CF'

intersect at the point

Y

. Prove that if

H

is the orthocenter of

\vartriangle ABC

, then the lines

AX, YH

, and

BC

are concurrent.