Given: circle a externally tangent to circle b.

a common internal tangent is

a. line r

b. line s

c. segment ab

Line r

Explanation:

A common internal tangent is a tangent of both circles in which the intersection of the tangent and the line segment joining the centers is not empty.

This means that the tangent and the line segment joining the centers must intersect.

Line s does not intersect AB, the line segment joining the circles.  This means line s is not the common internal tangent.

Segment AB is the segment joining the centers; it is not tangent to the circles.

Line r is tangent to both circles and intersects AB; this is the common internal tangent.