Let `C_1` be the circle of radius 1 with center at the origin. Let `C_2` be the circle of radius r with center at the point `A = (4,1)`, where `1 lt r lt 3`. Two distinct common tangents `PQ and ST` of `C_1` and `C_2` are drawn. The tangent `PQ` touches `C_1` at P and `C_2` at `Q`. The tangent `ST` touches `C_1` at `S` and `C_2` at T. Mid points of the line segments `PQ and ST` are joined to form a line which meets the x -axis at a point `B` . If `AB = sqrt5` , then the value of `r^2` is