Correct Option: B

On the basis of given in question , we draw a figure of an isosceles triangle ABC inscribed in a circle ,

AD ⊥ BC
Given , BC = 24 cm
BD = DC = 12 cm.
OC = OA = Circum-radius = r cm.
AD = √AB² - BD²
AD = √(12√5)² - (12)²
AD = √144 × 5 = 144
AD = √144(5 –1)
AD = √144 × 4 = 24 cm.
In ∆OCD,
OD = (24 – r) cm.
∴ OC² = OD² + CD²
⇒ r² = (24 – r)² + 12²
⇒ r² = 576 – 48r + r² + 144
⇒ 48r = 720
⇒ r = 720 ÷ 48 = 15 cm.