HMMT 2017 U18

Guts
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Let $A B C D$ be a quadrilateral with side lengths $A B=2, B C=3, C D=5$ , and $D A=4$ . What is the maximum possible radius of a circle inscribed in quadrilateral $A B C D$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2 \sqrt{30}}{7}

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