HMMT 2003 U25

Guts
Answer

Let $A B C$ be an isosceles triangle with apex $A$ . Let $I$ be the incenter. If $A I=3$ and the distance from $I$ to $B C$ is 2 , then what is the length of $B C$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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4 \sqrt{5}

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