Question

AB is tangent to circle O at B. Find the length of the radius, r, for AB = 5 and AO = 13.

Answer 1

ΔABO is a right triangle with AB⊥BO. The radius of the circle is BO. The Pythagorean theorem applies.
AO² = AB² + BO²
13² = 5² + r²
169 -25 = r²
r = √144 = 12

The radius (r) is 12.

Answer 2

the radius is twelve