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The distances from a point on the circumcircle of an equilateral triangle to the two nearest vertices are 3 and 6.     

Find the distance from the point to the furthest vertex.     

 

Draw it and the answer is obvious.  There's a third of the circle's circumference from each vertex to the next.     

From the point to the two nearest vertices is 3 to one and 6 to the other.  So a third of the circumference is 9.     

You start from the point and go the direction that's 6 to a vertex, and then it's 9 to the next vertex.  6 + 9 = 15     

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