I need to find the center circle with a radius R3, tangent to other two circles with radius R1 and R2 and centers X1, Y1 and X2,Y2.

Any help? Thanks in avance!

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- Dec 8th 2005, 03:00 PMHelder Barros[SOLVED] Center of a circle tangent to other two circles
I need to find the center circle with a radius R3, tangent to other two circles with radius R1 and R2 and centers X1, Y1 and X2,Y2.

Any help? Thanks in avance! - Dec 8th 2005, 08:33 PMCaptainBlackQuote:

Originally Posted by**Helder Barros**

from $\displaystyle (X_1,Y_1)$, and also at a distance of $\displaystyle R_2+R_3$ from $\displaystyle (X_2,Y_2)$.

Hence the centre is at the point of intersection of:

$\displaystyle (x-X_1)^2\ +\ (y-Y_1)^2\ =\ (R_1+R_3)^2$

and

$\displaystyle (x-X_2)^2\ +\ (y-Y_2)^2\ =\ (R_2+R_3)^2$

(note there can be zero one or two solutions to this, also this

is for exterior tangency, if $\displaystyle R_3$ is large enough we

can also have interior tangency which would require a change to

the RHS of the equations to $\displaystyle (R_3-R_1)^2$ and $\displaystyle (R_3-R_2)^2$ respectivly.

Now I think of it you can also have mixed interior

and exterior tangency)

RonL