Given:
a circle with a center O and a straight line with a point M on it(They do not intersect). Construct a circle tangent to the given circle and tangent at point M to the given line.
Using eulid tools?
Draw a line from the center of your circle to the point M on the line.
Construct the midpoint of the line(perpendic bisector) that will be the center of your new circle you will be directly between the two objects. Take your compass and place at the midpoint of the line you drew and open to point M draw a circle it will be tangent to both where you need them to be