5

Part of 2022 Taiwan TST Round 1

Problems(1)

Chasing After the Tangent

Source: 2022 Taiwan TST Round 1 Mock Day 2 P5

3/19/2022

Let

H

be the orthocenter of a given triangle

ABC

. Let

BH

and

AC

meet at a point

E

, and

CH

and

AB

meet at

F

. Suppose that

X

is a point on the line

BC

. Also suppose that the circumcircle of triangle

AH

and the line

AB

intersect again at

Y

, and the circumcircle of triangle

CFX

and the line

AC

intersect again at

Z

. Show that the circumcircle of triangle

AYZ

is tangent to the line

AH

.
Proposed by usjl

geometrycircumcircleTaiwan