MathDB

MN goes through fixed point

Source: Iran TST 2014, second exam, day 1, problem 2

January 1, 2015

geometryincentercircumcirclegeometric transformation

Problem Statement

Point

D

is an arbitary point on side

BC

of triangle

ABC

.

I

,

I_1

and

I_2

are the incenters of triangles

ABC

,

ABD

and

ACD

respectively.

M\not=A

and

N\not=A

are the intersections of circumcircle of triangle

ABC

and circumcircles of triangles

IAI_1

and

IAI_2

respectively. Prove that regardless of point

D

, line

MN

goes through a fixed point.

Back to Problems View on AoPS