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The diagonal of a parallelogram is trisected by...

Source: South Africa 2003

October 14, 2005

geometryparallelogramratio

Problem Statement

Given a parallelogram

ABCD

, join

A

to the midpoints

E

and

F

of the opposite sides

BC

and

CD

AE

and

AF

intersect the diagonal

BD

M

and

N

. Prove that

M

and

N

divide

BD

into three equal parts.