I can kill this question in 30 Seconds, can uou?

Geometry Level pending

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 \(S=0\) ?

I kill this question orally in a text book for IIT JEE, So I just wanted share this with our community! Hope you may also solved it in this time constrained.
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