Hi VJesus12,
We're told that in the figure above, an EQUILATERAL triangle is inscribed in a circle and the arc bounded by adjacent corners of the triangle is between 4Ï€ and 6Ï€ long. We're asked which of the following COULD be the diameter of the circle. As scary as this question might look, it's based on a couple of standard Geometry rules, so you can answer it with just a little work.
To start, an equilateral triangle has 3 equal angles - and since the triangle is inscribed in the circle, each of the three 'arc pieces' is equal in length. Thus, the total of those three arcs (re: the circumference of the circle) is between (3)(4Ï€) and (3)(6Ï€). If the total circumference is between 12Ï€ and 18Ï€, then we can 'work backwards' to find the possible diameter....
12π = 2π(R) = πD..... Diameter = 12
18π = 2π(R) = πD..... Diameter = 18
There's only one answer that's between 12 and 18...
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
