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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 ## What is the greatest possible area of a triangular region tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## What is the greatest possible area of a triangular region ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMAT Prep What is the greatest possible area of a triangular region with one vertex at the center of a circle with radius one and the other two vertices on the circle? $$A.\ \frac{ \sqrt{3}}{4}$$ $$B.\ \frac{1}{2}$$ $$C.\ \frac{\pi}{4}$$ $$D.\ 1$$ $$E.\ \sqrt{2}$$ OA B ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1114 messages Followed by: 29 members Upvotes: 59 AAPL wrote: GMAT Prep What is the greatest possible area of a triangular region with one vertex at the center of a circle with radius one and the other two vertices on the circle? $$A.\ \frac{ \sqrt{3}}{4} \,\,\,\,\,\,B.\ \frac{1}{2}\,\,\,\,\,\,C.\ \frac{\pi}{4}\,\,\,\,\,\,D.\ 1\,\,\,\,\,\,E.\ \sqrt{2}$$ $$?\,\,\, = \,\,{S_{\Delta ABC}}\,\,\max$$ Let C be the center of the circle with unitary radius. Without loss of generality, we may (and will) assume point A is one unit at the right of point C (as shown in the figure on the left). For the last vertex (B), without loss of generality (in terms of exploring possible areas) there are only two possibilities: (1) B is in the arc AD (figure in the middle) or (2) B is in the arc DE (figure on the right) In BOTH cases we have: $${S_{\Delta ABC}} = {{AC \cdot h} \over 2} = {h \over 2}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = {1 \over 2}\,\,\,\,\,\,\left( {{\rm{when}}\,\,h = CD\,,\,\,{\rm{i}}{\rm{.e}}{\rm{.}},\,\,B = D} \right)$$ This solution follows 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 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15023 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: GMAT Prep What is the greatest possible area of a triangular region with one vertex at the center of a circle with radius one and the other two vertices on the circle? $$A.\ \frac{ \sqrt{3}}{4}$$ $$B.\ \frac{1}{2}$$ $$C.\ \frac{\pi}{4}$$ $$D.\ 1$$ $$E.\ \sqrt{2}$$ OA B Given two sides of a triangle, the greatest possible area will be achieved if the two sides form a RIGHT ANGLE and serve as the triangle's base and height. For the problem above, I posted an illustrated solution here: https://www.beatthegmat.com/largest-possible-area-of-triangle-inside-circle-t274809.html _________________ 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. • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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