# Math Help - Construction help

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

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

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

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

$P$ is the center of the third circle.

Using $P$ as center and $r_3$ 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.