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AP = CQ wanted, axis of MN related, midpoints of AD,BC where AB=CD

Source: 2022 Oral Moscow Geometry Olympiad grades 8-9 p3

April 17, 2022

equal segmentsgeometry

Problem Statement

In quadrilateral

ABCD

, sides

AB

and

CD

are equal (but not parallel), points

M

and

N

are the midpoints of

AD

and

BC

. The perpendicular bisector of

MN

intersects sides

AB

and

CD

at points

P

and

Q

, respectively. Prove that

AP = CQ

.
(M. Kungozhin)