# known circle inside of a 60 degree angle?

• Apr 21st 2010, 03:39 AM
jonb
known circle inside of a 60 degree angle?
A friend of mine is trying to machine apart.

We have a circle of known diameter. Picture a this circle inside of a 60 degree angle. We need to know how far the tangents are from the corner of the angle.

How would we set this up.

Thanks
• Apr 21st 2010, 04:04 AM
jonb
Lets say the circle is one inch. There is a 60 degree angle. How far away is the corner of the angle from either of the tangents where the circle is contacting both side of the 60 degree angle.
• Apr 21st 2010, 05:54 AM
sa-ri-ga-ma
Quote:

Originally Posted by jonb
Lets say the circle is one inch. There is a 60 degree angle. How far away is the corner of the angle from either of the tangents where the circle is contacting both side of the 60 degree angle.

Corner of the angle , center and the point of contact of the tangent form a right angled triangle with 30-90-60 angles.
Now you can find easily relation between the sides and the length of the tangent.
• Apr 21st 2010, 07:05 AM
Soroban
Hello, jonb!

sa-ri-ga-ma has the best approach!

Quote:

We have a circle of known diameter.
Picture this circle inside of a 60° angle.
We need to know how far the tangents are from the corner of the angle.

How would we set this up?

Code:

```                  /                   /  * * *                 /*          *                 *              *               *                *               /             /*        O        *             / *        *        *           /  *      *  |        *           /      *    |         /    *        |r      *         /  *  *      |      *       / * 30°    *    |    *       * - - - - - - - * * *       A                B```

\$\displaystyle \Delta OBA\$ is a 30-60-90 right triangle.

We have: .\$\displaystyle \angle OAB = 30^o,\;OB = r\$

You can now find \$\displaystyle AB.\$