MathDB

lines through parallelogram independent of choice of parallelogram

Source: Croatia MO 2001 3rd Grade P1

April 22, 2021

geometryparallelogram

Problem Statement

Let

O

and

P

be fixed points on a plane, and let

ABCD

be any parallelogram with center

O

. Let

M

and

N

be the midpoints of

AP

and

BP

respectively. Lines

MC

and

ND

meet at

Q

. Prove that the point

Q

lies on the lines

OP

, and show that it is independent of the choice of the parallelogram

ABCD