It is known that there are three points a and B. C on the sphere, which form an equilateral triangle with side length of 1. If the distance from the center of the sphere to the plane ABC is equal to 13 of the radius of the sphere, then the radius of the sphere is () A. 3B. 13C. 64D. 32

Let the center of the circumscribed circle of △ ABC be o ', then Ao' = 23ad = 33, and let the center of the sphere be o, because the distance from the center of the sphere o to the plane ABC is equal to 13 of the radius of the sphere, so OO '= 13oa. In RT △ oo'a, o'a2 + OO'2 = oa2, that is, (33) 2 + 19

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