159

Part of 1972 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 159 All Soviet Union MO 1972 rectangle <QNM=<MNP wanted

Source:

Given a rectangle

ABCD

M

-- the midpoint of

[AD]

N

-- the midpoint of

[BC]

side. Let us take a point

P

on the extension of the

[DC]

segment over the point

D

. Let us denote the intersection point of lines

(PM)

(AC)

Q

. Prove that the

\angle QNM= \angle MNP

geometryrectangleequal angles