SOLUTION: Given: Two concentric circles with tangent to smaller circle at R Prove: AR = RB

You can put this solution on YOUR website!

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