MathDB

USAMO 2003 Problem 4

Source:

September 27, 2005

AMCUSA(J)MOUSAMOgeometryparallelogramcircumcircle

Problem Statement

Let

ABC

be a triangle. A circle passing through

A

and

B

intersects segments

AC

and

BC

at

D

and

E

, respectively. Lines

MB\cdot MD = MC^2

and

DE

intersect at

F

, while lines

BD

and

CF

intersect at

M

. Prove that

MF = MC

if and only if

MB\cdot MD = MC^2

.

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