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Incenter and excenter

Source: Cono Sur Olympiad 2016, problem 5

August 28, 2017

geometrycono surincenter

Problem Statement

Let

ABC

be a triangle inscribed on a circle with center

O

. Let

D

and

E

be points on the sides

AB

and

BC

,respectively, such that

AD = DE = EC

. Let

X

be the intersection of the angle bisectors of

\angle ADE

and

\angle DEC

. If

X \neq O

, show that, the lines

OX

and

DE

are perpendicular.

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