Points C and D are on a circle O with a diameter of AB, and CD bisects ∠ACB. If AB = 2, ∠ CBA = 15, what is the length of the CD?

Add OC, OC=OB.

So ∠ OBC = ∠ OCB = 15.

Because AB is the diameter, ACB = 90.

Because the CD score is ∠ACB, ∠ BCD = 45.

∠OCD=∠BCD-∠OCB=45 - 15 =30

AB=2,r= 1,OC= 1

So CD=√3