# [SOLVED] Center of a circle tangent to other two circles

• Dec 8th 2005, 03:00 PM
Helder 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 PM
CaptainBlack
Quote:

Originally Posted by Helder Barros
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!

The centre of the required circle is at a distance of $R_1+R_3$
from $(X_1,Y_1)$, and also at a distance of $R_2+R_3$ from $(X_2,Y_2)$.

Hence the centre is at the point of intersection of:

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

and

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

(note there can be zero one or two solutions to this, also this
is for exterior tangency, if $R_3$ is large enough we
can also have interior tangency which would require a change to
the RHS of the equations to $(R_3-R_1)^2$ and $(R_3-R_2)^2$ respectivly.
Now I think of it you can also have mixed interior
and exterior tangency)

RonL