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)

Quote:

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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)

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The line is the radical axis.

Thanks thats interesting.
Is there a proof though?