What is the length of the tangent drawn from any point of the circle x2+y2+2gx+2fy+c=0 to the circle x2+y2+2gx+2fy+d=0 ?

Hi Sohan,

Let (a,b) be any point on the circle, from where the tangent is drawn to the other circle.

(a,b) would satisfy the eqn of the first circle.

Let of tangent from any point (a,b) to the second ciscle is √(S1)

where S1 is obtained by substituting (a,b) in the second equation.

So S1 = a²+b²+2ga+2fb+c.

But a²+b²+2ga+2fb+ d = 0.

So S1 = c-d.

So length of tangent = √(c-d).

Best Regards,

Ashwin (IIT Madras).

Approved

the two eqn clearly represent concentric circles as they have centrs at (-g,-f) .
Now
x²+y²+2gx+2fy+c=0   ....... 1
x²+y²+2gx+2fy+d=0  ........2


Eqn 1 repesent circle wid larger radius n the latter(2) represent smaller radius.
Both the cir