# Non intersecting circles...

• Sep 29th 2011, 06:47 AM
rodders
Non intersecting circles...
Ok ,

Suppose you take two circles and they do not intersect:
e.g

x^2 + y^2 -6x-6y+14=0
x^2 +y^2 +6x+4y+12 =0

If you subtract the two equations you get a line:

-12x-10y+2=0

Now, if we chose any point P on this line, then the lengths of the tangents from P to each of the circles are equal?

Why and how do we prove this?

(I know that that if the intersected, the line would represent a common chord)
• Sep 29th 2011, 08:44 AM
alexmahone
Re: Non intersecting circles...
Quote:

Originally Posted by rodders
Ok ,

Suppose you take two circles and they do not intersect:
e.g

x^2 + y^2 -6x-6y+14=0
x^2 +y^2 +6x+4y+12 =0

If you subtract the two equations you get a line:

-12x-10y+2=0

Now, if we chose any point P on this line, then the lengths of the tangents from P to each of the circles are equal?

Why and how do we prove this?

(I know that that if the intersected, the line would represent a common chord)

The line is the radical axis.
• Sep 29th 2011, 01:23 PM
rodders
Re: Non intersecting circles...
Thanks thats interesting.
Is there a proof though?