MathDB

G5

Part of 2009 Balkan MO Shortlist

Problems(1)

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

Source: 2009 Balkan Shortlist BMO G5 - easy / medium

4/5/2020
Let ABCDABCD be a convex quadrilateral and SS an arbitrary point in its interior. Let also EE be the symmetric point of SS with respect to the midpoint KK of the side ABAB and let ZZ be the symmetric point of SS with respect to the midpoint LL of the side CDCD. Prove that (AECZ)=(EBZD)=(ABCD)(AECZ) = (EBZD) = (ABCD).
areasequal areasSymmetricconvex quadrilateralmidpointgeometry