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Difference between revisions of "2022 SSMO Speed Round Problems/Problem 3"

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==Problem==
  
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Let <math>ABCD</math> be a parallelogram such that <math>E</math> is a point on <math>CD</math> such that <math>\frac{CE}{DE}=\frac{2}{3}.</math> Suppose that <math>BE</math> and <math>AC</math> intersect at <math>F.</math> If the area of triangle <math>AEF</math> is <math>15,</math> find the area of <math>ABCD</math>.
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==Solution==

Latest revision as of 19:14, 2 May 2025

Problem

Let $ABCD$ be a parallelogram such that $E$ is a point on $CD$ such that $\frac{CE}{DE}=\frac{2}{3}.$ Suppose that $BE$ and $AC$ intersect at $F.$ If the area of triangle $AEF$ is $15,$ find the area of $ABCD$.

Solution

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