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Angle Bisectors in Triangle

Source: 2009 IrMO Paper 2 Problem 5

January 30, 2018

geometryangle bisector

Problem Statement

In the triangle

ABC

we have

|AB|<|AC|

. The bisectors of the angles at

B

and

C

meet

AC

and

AB

at

D

and

E

respectively.

BD

and

CE

intersect at the incenter

I

of

\triangle ABC

.
Prove that

\angle BAC=60^\circ

if and only if

|IE|=|ID|

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