Let $A B C$ be the triangle with $A B=1, A C=3$ and $\angle B A C=\frac{\pi}{2}$. If a circle of radius $r>0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$, then what is the value of $r$?
JEE · Math · previous-year question
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