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UKMT Mathematical Olympiad for Girls, 2014

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

A chord of a circle has length $3n$ , where $n$ is a positive integer. The segment cut off by the chord has height $n$ , as shown.

What is the smallest value of $n$ for which the radius of the circle is also a positive integer?

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