MathDB

concurrent lines formed by incenter and excenters

Source: Iran 3rd round 2011-geometry exam-p5

September 6, 2011

geometryincentercircumcirclegeometric transformationangle bisectorgeometry proposed

Problem Statement

Given triangle

ABC

D

is the foot of the external angle bisector of

A

I

its incenter and

I_a

its

A

-excenter. Perpendicular from

I

DI_a

intersects the circumcircle of triangle in

A'

. Define

B'

and

C'

similarly. Prove that

AA',BB'

and

CC'

are concurrent.
proposed by Amirhossein Zabeti