# How to calculate a circle's radius when tangent to 2 intersecting lines

• March 24th 2010, 01:46 PM
Involute
How to calculate a circle's radius when tangent to 2 intersecting lines
In the diagram below, circle c is tangent to lines p, q, and r. Lines q and s are perpendicular to each other. Angle a is 20 degrees (the subtended angle is 40 degrees). What is the radius of circle c, and how did you calculate it? Thanks.

Involute

http://www.lautman.com/CrankCalc.jpg
• March 24th 2010, 02:26 PM
Plato
If I understand the diagram correctly, this is true.
$\sin(20^o)=\frac{r}{1-r}$.
• March 24th 2010, 02:37 PM
Involute
Looks right to me. Thanks!