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

1. ## 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

2. If I understand the diagram correctly, this is true.
$\sin(20^o)=\frac{r}{1-r}$.

3. Looks right to me. Thanks!