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2025 SSMO Speed Round Problems/Problem 4

Revision as of 11:10, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== In rectangle <math>ABCD,</math> let <math>AB = 8,BC = 15,\omega</math> be the circumcircle of <math>ABCD</math>, <math>\ell</math> be the line through <math>B</ma...")
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Problem

In rectangle $ABCD,$ let $AB = 8,BC = 15,\omega$ be the circumcircle of $ABCD$, $\ell$ be the line through $B$ parallel to $AC,$ and $X \neq B$ be the intersection of $\ell$ and $\omega$. Suppose the value of $BX$ can be expressed as $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Solution

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