MathDB

Given an acute and scalene triangle

ABC

, let

H

be its orthocenter,

O

its circumcenter,

E

and

F

the feet of the altitudes drawn from

B

and

C

, respectively. Line

AO

intersects the circumcircle of the triangle again at point

G

and segments

FE

and

BC

at points

X

and

Y

respectively. Let

Z

be the point of intersection of line

AH

and the tangent line to the circumcircle at

G

. Prove that

HX

is parallel to

YZ

Problem Statement