AE = BE = 5
CF = FD = 12
EF = 17
OE = x, Then OF = 17-x

OAE is a right angle triangle, Apply Pythagorean theorem,
OA = $\sqrt{25+x^2}$ = radius
Similarly, OCF is a right angle triangle, Apply Pythagorean theorem,
OC = $\sqrt{(17-x)^2+144}$ = radius

Equating both equations as both are the radii, we get
$25+x^2 = 289+x^2-34x+144$
34x = 408
x = 12 = OE, then OF = 5
OA = OC = $\sqrt{25+144}$ = 13

C is the answer.