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)

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.

Re: Non intersecting circles...

Thanks thats interesting.

Is there a proof though?