1. ## Construction help

I need help constructing three circles that are externally tangent to each other, however, the circles are already given to me. Two of the circles are already externally tangent, I have to take the third and make it externally tangent to both, so ultimately I'll have three circles, all externally tangent to one another.

Thanks in advance for any help.

2. Hello, njgrillo!

I need help constructing three circles that are externally tangent to each other.
The circles are already given to me.
Two of the circles are already externally tangent.
I have to make the third circle externally tangent to both.
I'll try to explain this without a diagram . . .

We have a circle with center $\displaystyle C_1$ and radius $\displaystyle r_1$.
We have a circle with center $\displaystyle C_2$ and radius $\displaystyle r_2$.
. . These are externally tangent.

We have a third circle with radius $\displaystyle r_3$.
We want it to be externally tangent to both $\displaystyle C_1$ and $\displaystyle C_2$.

Using $\displaystyle C_1$ as center, draw an arc with radius $\displaystyle r_1+r_3$

Using $\displaystyle C_2$ as center, draw an arc with radius $\displaystyle r_2+r_3$
. . intersecting the first arc at point $\displaystyle P.$

$\displaystyle P$ is the center of the third circle.

Using $\displaystyle P$ as center and $\displaystyle r_3$ as radius, draw the third circle.

3. Originally Posted by njgrillo
I need help constructing three circles that are externally tangent to each other, ...

Thanks in advance for any help.
According to Soroban's description I've made the sketch.