The lines AB and L intersect at a fixed point P.
The circle we search has centre at O . and the line L is tangent to this circle at the point Q.
According to a well known theorem of the Euclidean Geometry (PA) X (PB) = (PQ)^2 therefore PQ =SQRROOT[(PA) X (PB)]
this expression defines the position of the point of tangency Q along the line L . The centre of the circle is the intersection point O of the perpendicular bisector of AB and the perpendicular line to the line L at Q. OA =OB =OQ = r is the radius of the circle .