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ASU 312 All Soviet Union MO 1981 (KLMN) =1/2 (ABCD), areas

Source:

July 23, 2019

geometryrectangle

Problem Statement

The points

K

and

M

are the centres of the

AB

and

CD

sides of the convex quadrangle

ABCD

. The points

L

and

M

belong to two other sides and

KLMN

is a rectangle. Prove that

KLMN

area is a half of

ABCD

area.