What is the radius of the circle with center A ?(1) BC =

2\sqrt{3}. We have the length of a chord, which is clearly insufficient to answer the question. Not sufficient.

(2) Angle BCA has a measure of 30°. Notice that since AB = AC = radius, then triangle ABC is isosceles, which means that angles at B and C are equal. So, we have that angle B = angle C = 30° and angle A = 180 - (30 + 30) = 120°. We know all the angles in ABC but we don't know any of the lengths. Not sufficient.

(1)+(2) We know all the angles in ABC and the length of one of the sides, BC. So, we can find any other length there, including AC (radius). Sufficient.

Answer: C.

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