Please help me with solveing this system of equations?

Question

Ok, in order to see the equation properly you can look at the pic at the link.

http://i4.photobucket.com/albums/y117/imunalia/equ2.png

Link to Equations sqrt((X1-X3)^2+(Y1-Y3)^2)=D1 sqrt((X2-X3)^2+(Y2-Y3)^2)=D2 I need to solve X3 and Y3 I'm basically looking for a co-ordinate solution for the intersection of 2 circles with two different radii. Any help is appreciated.

The circles are centered at X1,Y1 and X2, Y2

D1 and D2 are the diameters. X3, Y3 can be solved for as long as D1 + D2 is > than the distance between the two centers

Answer 1

sqrt((X1-X3)^2+(Y1-Y3)^2)=D1 sqrt((X2-X3)^2+(Y2-Y3)^2)=D2

if you have the intersection of 2 circles:
(x-a)^2 +(y-b)^2 = d1^2
(x-m)^2 + (y-n)^2 =d2^2
then
you try to write one variable in terms of the other
and then substitute in the other equation

if they have the same center, then
the circles DO NOT intersect at all, unless d1=d2, in which case it is exactly the same circle.
s

Answer 2

It looks to me like both circles are centered at (x3,y3), is that right? If so, then they won't intersect unless they're identical. I must be missing something.