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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 percent of the area of the rhombus ABCD is the area of tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## What percent of the area of the rhombus ABCD is the area of ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 19) What percent of the area of the rhombus ABCD is the area of the circle that is inscribed in it? (1) Angle BCD is equal to 60 degrees (2) AB = 4 Answer: _____(A)__ _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 19) What percent of the area of the rhombus ABCD is the area of the circle that is inscribed in it? (1) Angle BCD is equal to 60 degrees (2) AB = 4 $$? = {{{S_{{\rm{circle}}}}} \over {{S_{{\rm{rhombus}}}}}}$$ $$\left( 1 \right)\,\,\,\left\{ \matrix{ BCD = {60^ \circ } \hfill \cr ABCD\,\,{\rm{rhombus}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta \,CBD\,\,{\rm{and}}\,\,\Delta ABD\,\,{\rm{equilaterals}}\,\,\,\left( * \right)\,\,\,\,\,$$ $$?\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{S_{{\text{circle}}}}}}{{2 \cdot {S_{\Delta {\text{ABD}}}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{\pi \cdot O{E^2}}}{{2 \cdot \left( {\frac{1}{2} \cdot BD \cdot \frac{{BD \cdot \sqrt 3 }}{2}} \right)}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,? = {\left( {\frac{{OE}}{{BD}}} \right)^2}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\boxed{\,? = \frac{{OE}}{{BD}}\,}$$ $$\left\{ \matrix{ \,\Delta OEB\,\,\,\,\left[ {{{30}^ \circ },{{60}^ \circ },{{90}^ \circ }} \right] \hfill \cr \,{1 \over 2}BD = OB\,\,\,{\rm{hyp}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left[ {{{30}^ \circ },{{60}^ \circ },{{90}^ \circ }} \right]} \,\,\,\,OE = {{OB \cdot \sqrt 3 } \over 2} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {{OE} \over {BD}} = {{OE} \over {2 \cdot OB}} = {1 \over 2}\left( {{{\sqrt 3 } \over 2}} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$ $$\left( 2 \right)\,\,{\rm{Insuff}}.\,\,\,\,\left( {{\rm{geometric}}\,\,{\rm{bifurcation}}\,{\rm{,}}\,\,{\rm{see}}\,\,{\rm{images}}} \right)$$ The correct answer is (A). 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free 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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