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2023 WSMO Accuracy Round Problems/Problem 6

Revision as of 15:35, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== In quadrilateral <math>ABCD,</math> there exists a point <math>O</math> such that <math>AO = BO = CO = DO</math> and <math>\angle(AOB)+\angle(COD) = 120^{\circ}.<...")
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Problem

In quadrilateral $ABCD,$ there exists a point $O$ such that $AO = BO = CO = DO$ and $\angle(AOB)+\angle(COD) = 120^{\circ}.$ Let $K,L,M,N$ be the foot of the perpendiculars from $A$ to $BD,$ $B$ to $AC,$ $C$ to $BD,$ and $D$ to $AC.$ If $[ABCD] = 20,$ find $\left([KLMN]\right)^2.$

Solution

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