let the common center of the two circles be O.
Draw radii OA and OB of the larger circle and radius OR of
the smaller circle.



I won't write it in a 2-line proof.  I'll just tell you what
to do and you can write it up as a 2-line proof.

OA = OB because they are radii of the same (larger) circle

OR is perpendicular to AB, because a tangent to a circle is
perpendicular to the radius drawn to the point of tangency.

So triangles ARO and BRO are right triangles.

OR = OR

Right triangles ARO and BRO are congruent because they have
a pair of congruent hypotenuses and a pair of congruent legs.

Therefore AR = RB because they are corresponding parts of 
congruent triangles.

Edwin