MathDB

Romania NMO 2023 Grade 7 P2

Source: Romania National Olympiad 2023

April 14, 2023

geometrysimilar trianglesMenelaus

Problem Statement

In the parallelogram

ABCD

,

AC \cap BD = { O }

, and

M

is the midpoint of

AB

. Let

P \in (OC)

and

MP \cap BC = { Q }

. We draw a line parallel to

MP

from

O

, which intersects line

CD

at point

N

. Show that

A,N,Q

are collinear if and only if

P

is the midpoint of

OC

.

Back to Problems View on AoPS