Calculating internal radius with known boundaries

Imagine using a round end lathe tool to manufacture a round feature tangent to the work piece’s abutment face and a given depth to intersect a diameter.Such a situation is a simple relief for simple face grinding (see figure below).

 If we call A the width dimension, R the unknown radius and B the given depth, then the geometry that describes them is:

For calculating the unknown radius with known boundaries of A & B passing through run out point and tangent to two surfaces, we must use the Pythagoras Theorem and the solution of quadratic equation:

Since radius R must be less than dimension A we accept only one solution of the above formula.