SHARYGIN 2006 Problem 6

a) Given a segment $AB$ with a point $C$ inside it, which is the chord of a circle of radius $R$ . Inscribe in the formed segment a circle tangent to point $C$ and to the circle of radius $R$ . b) Given a segment $AB$ with a point $C$ inside it, which is the point of tangency of a circle of radius $r$ . Draw through $A$ and $B$ a circle tangent to a circle of radius $r$ .