A circle $S=0$ passes through the point of intersection of two circles: $\displaystyle{{ S }_{ 1 }:\quad { x }^{ 2 }+{ y }^{ 2 }-3x+4y+5=0\\ { S }_{ 2 }:\quad { x }^{ 2 }+{ y }^{ 2 }-4x+3y+5=0}$

Circle $S=0$ also cuts the circle ${ S }_{ 3 }:\quad { x }^{ 2 }+{ y }^{ 2 }=4$ orthogonally.

Compute the value of length of tangent from origin to the circle $S=0$ ?