Construction help

• Apr 26th 2009, 02:29 PM
njgrillo
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.
• Apr 27th 2009, 05:11 AM
Soroban
Hello, njgrillo!

Quote:

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.

• Apr 27th 2009, 05:21 AM
earboth
Quote:

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.