When I read this question, the first thing that struck me as odd was that they mentioned "CD is a positive integer" (which presumably means that the length of CD is a positive integer)
Length would obviously be positive but needn't be an integer. If it is specified and seeing that OCD is a right triangle (tangent makes 90 degree angle with radius), this might have something to do with pythagorean triplets.
The ones with 15 or factors of 15 (since OC = 15) are
3, 4, 5 (the sides can be 15, 20, 25)
5, 12, 13 (the sides can be 15, 36, 39)
8, 15, 17 (the sides can be 8, 15, 17)
(OC is one leg and CD is the other)
The only length given in the options is 20 (we have neither 36 nor 8)
Answer (C)
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