MathDB

(AECZ) = (EBZD) = (ABCD) , equal areas

Source: 2009 Balkan Shortlist BMO G5 - easy / medium

April 5, 2020

areasequal areasSymmetricconvex quadrilateralmidpointgeometry

Problem Statement

Let

ABCD

be a convex quadrilateral and

S

an arbitrary point in its interior. Let also

E

be the symmetric point of

S

with respect to the midpoint

K

of the side

AB

and let

Z

be the symmetric point of

S

with respect to the midpoint

L

of the side

CD

. Prove that

(AECZ) = (EBZD) = (ABCD)