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Excircle-related intersection on Thales circle of BC

Source: ITAMO 2016, Problem 3

May 11, 2016

geometry

Problem Statement

Let

\Gamma

be the excircle of triangle

ABC

opposite to the vertex

A

(namely, the circle tangent to

BC

and to the prolongations of the sides

AB

and

AC

from the part

B

and

C

). Let

D

be the center of

\Gamma

and

E

,

F

, respectively, the points in which

\Gamma

touches the prolongations of

AB

and

AC

. Let

J

be the intersection between the segments

BD

and

EF

.
Prove that

\angle CJB

is a right angle.

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