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N is inside the quadrilateral abcd

Source: IMO Shortlist 1994, G2

October 22, 2005

geometryquadrilateralmidpointsIMO Shortlist

Problem Statement

ABCD

is a quadrilateral with

BC

parallel to

AD

.

M

is the midpoint of

CD

,

P

is the midpoint of

MA

and

Q

is the midpoint of

MB

. The lines

DP

and

CQ

meet at

N

. Prove that

N

is inside the quadrilateral

ABCD

.

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