HMMT 2007 F10

General 2
Answer

$A B C D$ is a convex quadrilateral such that $A B=2, B C=3, C D=7$ , and $A D=6$ . It also has an incircle. Given that $\angle A B C$ is right, determine the radius of this incircle.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1+\sqrt{13}}{3}

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