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2022 SSMO Accuracy Round Problems/Problem 8

Revision as of 13:03, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>ABCD</math> be a trapezoid with <math>AB \parallel CD</math>. Suppose that <math>AD=1</math>, <math>DC=4</math>, <math>CB=2</math>, and <math>AB<CD</math...")
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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 $m+n.$

Solution

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