2022 SSMO Accuracy Round Problems/Problem 8

Problem

Let $ABCD$ be a trapezoid with $AB \parallel CD$ . Suppose that $AD=1$ , $DC=4$ , $CB=2$ , and $AB<CD$ . Let $X$ be the midpoint of $AB$ . If $E$ is the intersection of $AC$ and $BD$ , and $\angle XEB=\angle ADC$ , then $AB=\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n.$

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2022 SSMO Accuracy Round Problems/Problem 8

Problem

Solution