MathDB

Prove that PE/PF=ME/NF - Iran NMO 2007 - Problem5

Source:

September 22, 2010

geometrygeometry proposed

Problem Statement

Tow circles

C,D

are exterior tangent to each other at point

P

. Point

A

is in the circle

C

. We draw

2

tangents

AM,AN

from

A

to the circle

D

(

M,N

are the tangency points.). The second meet points of

AM,AN

with

C

are

E,F

, respectively. Prove that

\frac{PE}{PF}=\frac{ME}{NF}