MathDB

collinear wanted, 2 parallelograms related

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2010 Seniors p3

September 6, 2020

geometryparallelogramcollinearChampions Tournament

Problem Statement

On the sides

AB

and

BC

arbitrarily mark points

M

and

N

, respectively. Let

P

be the point of intersection of segments

AN

and

BM

. In addition, we note the points

Q

and

R

such that quadrilaterals

MCNQ

and

ACBR

are parallelograms. Prove that the points

P,Q

and

R

lie on one line.