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Iran TST 2015 Geometry

Source: Iran TST 2015,third exam,second day,problem 6

May 29, 2015

geometrymoving points

Problem Statement

AH

is the altitude of triangle

ABC

and

H^\prime

is the reflection of

H

trough the midpoint of

BC

. If the tangent lines to the circumcircle of

ABC

at

AC

and

C

, intersect each other at

X

and the perpendicular line to

XH^\prime

at

H^\prime

, intersects

AB

and

AC

at

Y

and

Z

respectively, prove that

\angle ZXC=\angle YXB

.

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