2023 SSMO Accuracy Round Problems/Problem 4

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 $C$ )

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2023 SSMO Accuracy Round Problems/Problem 4

Problem

Solution