If point p is on line R, what is the total number of points 3 centimeters from point p and 4 centimeters from line R?
All points which have the distance of 4 cm from the line R are placed on 2 parallels of R with a perpendicular distance of 4 cm.
The parallels and the circle don't have common points because the radius is smaller than the perpendicular distance.
Therefore the answer is zero.
And as I look further, any point along the arc AB and arc CD with the exception of the intersection points of line R and the circle can be made to be 3 cm from P and 4 cm from line R. So my reasoning may be flawed. Otherwise, there's an infinite number of points that satisfy the condition specified.