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2023 SSMO Accuracy Round Problems/Problem 4

Revision as of 21:21, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== In square <math>ABCD,</math> point <math>E</math> is selected on diagonal <math>AC.</math> Let <math>F</math> be the intersection of the circumcircles of triangles...")
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Problem

In square $ABCD,$ point $E$ is selected on diagonal $AC.$ Let $F$ be the intersection of the circumcircles of triangles $ABE$ and $CDE.$ Given that $AB = 10$ and $EF = 6,$ find the maximum possible area of triangle $BEC.$ (A circumcircle of some triangle $\triangle ABC$ is the circle containing $A$, $B$, and $C$)

Solution

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