2024 SSMO Accuracy Round Problems/Problem 4

Problem

Right triangle $ABC$ has a right angle at $C$ and hypotenuse $1$ . Let points $D$ and $E$ lie on $AC$ such that $\angle BDC=\angle BEC=45^{\circ}$ . $A,D,C,$ and $E$ are colinear in that order. Given that $EA=13DA$ , the area of $\triangle ABC$ can be expressed as $\frac{m}{n}$ for relatively prime $m$ and $n$ . Find $m+n$ .

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2024 SSMO Accuracy Round Problems/Problem 4

Problem

Solution