MathDB

They are concurrent

Source: Iran 2002

April 9, 2004

geometrycircumcircle

Problem Statement

Circles

C_{1}

and

C_{2}

are tangent to each other at

K

and are tangent to circle

C

at

M

and

N

. External tangent of

C_{1}

and

C_{2}

intersect

C

at

A

and

B

.

AK

and

BK

intersect with circle

C

at

E

and

F

respectively. If AB is diameter of

C

, prove that

EF

and

MN

and

OK

are concurrent. (

O

is center of circle

C

.)

Back to Problems View on AoPS