To construct a circle with a given radius and touching the two given intersecting lines
- Draw two lines AB and AC at some angle say α.
- Draw bisector of ∠BAC.
- Construct a line parallel to line AB at a distance R (radius of the circle to be constructed(http://mathematicsbhilai.blogspot.in/2012/08/construction-of-parallel-line.html). Let this line intersect the angle bisector at point O.
- Draw a circle with center O and Radius R. This is the required circle.