Track / Stage 5 / 291 of 400 #891 of 1964

Problem 891

AIME late

Geometry Difficulty 5.6 Prove it

In a convex quadrilateral $ABCD$ , the line segments connecting the midpoints of opposite sides intersect at $O$ . Prove that:
$S_{\triangle AOB}+ S_{\triangle COD}=\frac{1}{2} S_{ABCD}$

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.