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An geometry problem from China TST

Source: China TST 4 Problem 2

March 23, 2017

geometryTST

Problem Statement

In

\varDelta{ABC}

,the excircle of

A

is tangent to segment

BC

,line

AB

and

AC

at

E,D,F

respectively.

EZ

is the diameter of the circle.

B_1

and

C_1

are on

DF

, and

BB_1\perp{BC}

,

CC_1\perp{BC}

.Line

ZB_1,ZC_1

intersect

BC

at

X,Y

respectively.Line

EZ

and line

DF

intersect at

H

,

ZK

is perpendicular to

FD

at

K

.If

H

is the orthocenter of

\varDelta{XYZ}

,prove that:

H,K,X,Y

are concyclic.

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