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HMMT 2008 U2

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Given right triangle ABCA B C, with AB=4,BC=3A B=4, B C=3, and CA=5C A=5. Circle ω\omega passes through AA and is tangent to BCB C at CC. What is the radius of ω\omega ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{25}{8}

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