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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In the figure above, an equilateral triangle is inscribed tagged by: VJesus12 ##### This topic has 2 expert replies and 0 member replies ## In the figure above, an equilateral triangle is inscribed ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In the figure above, an equilateral triangle is inscribed in a circle. If the arc bounded by adjacent corners of the triangle is between 4π and 6π long, which of the following could be the diameter of the circle? (A) 6.5 (B) 9 (C) 11.9 (D) 15 (E) 23.5 OA=D Source: Manhattan GMAT ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10071 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 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 4π and 6π 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)(4π) and (3)(6π). If the total circumference is between 12π and 18π, 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 _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2012 messages Followed by: 14 members Upvotes: 43 VJesus12 wrote: In the figure above, an equilateral triangle is inscribed in a circle. If the arc bounded by adjacent corners of the triangle is between 4π and 6π long, which of the following could be the diameter of the circle? (A) 6.5 (B) 9 (C) 11.9 (D) 15 (E) 23.5 OA=D Source: Manhattan GMAT Since each arc is bounded by adjacent corners of the triangle representing 1/3 of the circumference, the range of values of the circumference is: Minimum: 1/3(C) = 4π C = 12π, so the diameter would be 12. Maximum: 1/3(C) = 6π C = 18π, so the diameter would be 18. The diameter is between 12 and 18, so a possible diameter is 15. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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