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SMO 2019 Senior Round 1 Question 12

SMO · SMO 2019 Senior Round 1

Question 12

In the figure below, the chord $AF$ passes through the origin $O$ of the circle, and is perpendicular to the chord $BC$. It is given that $AB=17$ cm, $CD=5$ cm. Suppose $\frac{BE}{ED}=\frac mn$, where $m$ and $n$ are positive integers which are relatively prime. What is the value of $m+n$?

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