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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 shown, AB = AC = 12. Which of the following is tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## In the figure shown, AB = AC = 12. Which of the following is ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 7) In the figure shown, AB = AC = 12. Which of the following is closest to the area of the circle with center O that is tangent, at points M, N, and P, to the circular sector ABPC with center A and central angle of 60 degrees? (A) 40.1 (B) 43.7 (C) 46.8 (D) 50.2 (E) 53.7 Answer: ____(D)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 fskilnik@GMATH wrote: [size=17]GMATH practice exercise (Quant Class 7) In the figure shown, AB = AC = 12. Which of the following is closest to the area of the circle with center O that is tangent, at points M, N, and P, to the circular sector ABPC with center A and central angle of 60 degrees? (A) 40.1 (B) 43.7 (C) 46.8 (D) 50.2 (E) 53.7 AOP passes through the center of the inscribed circle and thus must BISECT sector ACB. AB, AP and AC are all radii of sector ACB and thus are equal. The prompt indicates AB=AC=12. Thus: AP=12. As shown in the figure, AOM is a 30-60-90 triangle Since OM is a radius of the circle, let OM = r. In a 30-60-90 triangle, the hypotenuse is twice the shorter leg. OM is opposite the 30-degree angle in triangle AOM and thus is the shorter leg. Since OM=r, hypotenuse AO=2r, with the result that AP = 2r+r = 3r. Since AP=12, we get: 3r = 12 r = 4. Thus, the area of the inscribed circle = Ï€rÂ² = Ï€(4Â²) â‰ˆ 50. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 7) In the figure shown, AB = AC = 12. Which of the following is closest to the area of the circle with center O that is tangent, at points M, N, and P, to the circular sector ABPC with center A and central angle of 60 degrees? (A) 40.1 (B) 43.7 (C) 46.8 (D) 50.2 (E) 53.7 $$?\,\, \cong \,\,\pi {r^2}$$ Point O is equidistant from the rays AM and AN, hence AO must be contained in the angle bisector of angle MAN = angle BAC. $$\left\{ \matrix{ \,OM = r\,\,\,\left( {{{30}^ \circ }} \right) \hfill \cr \Delta AOM\,\,\,\left( {{{30}^ \circ },{{60}^ \circ },{{90}^ \circ }} \right) \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,AO = 2r$$ Point P also belongs to the ray AO (by symmetry in the arc BPC) and AP=AB=12. Therefore: $$12 = AP = AO + OP = 3r\,\,\,\,\, \Rightarrow \,\,\,\,\,r = 4$$ $$?\,\, = \,\,16\pi \,\, \cong \,\,\left( {14 + 2} \right) \cdot {{22} \over 7}\,\, = \,\,44 + {{42 + 2} \over 7} = 50{2 \over 7}$$ The correct answer is (D). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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