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 $1<r<3.$  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   $AB=\sqrt{5},$then the value of  $r^2$  is