# 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 \$\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.

• 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.