Circle

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 the value of \(r\) is __________ .