MathDB

Ibero American 2012 - Problem 5

Source:

October 3, 2012

geometryincentersymmetrygeometric transformationhomothetyparallelogramangle bisector

Problem Statement

Let

ABC

be a triangle,

P

and

Q

the intersections of the parallel line to

BC

that passes through

A

with the external angle bisectors of angles

B

and

C

, respectively. The perpendicular to

BP

at

P

and the perpendicular to

CQ

at

Q

meet at

R

. Let

I

be the incenter of

ABC

. Show that

AI = AR

.

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