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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 ## A bigger circle (with center A) and a smaller circle tagged by: AAPL ##### This topic has 1 expert reply and 1 member reply ### Top Member ## A bigger circle (with center A) and a smaller circle ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: e-GMAT A bigger circle (with center A) and a smaller (circle with center B) are touching each other externally. PT and PS are tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST? (1) The radii of the bigger and the smaller circles are 9cm and 4cm respectively. (2) PB = 52/5 cm. The OA is A. Is there a strategic approach to this question? Can anyone help? Thanks! ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 786 messages Followed by: 1 members Given that PT is a tangent to the small circle and PS is a tangent to the big circle DPTB and DPSA are right -angled at T and S respectively. Question = Find the length of ST. Statement 1 = The radius of the bigger and smaller circles are 9cm and 4cm respectively . This makes the distance between AS = 9cm and BT =4cm. By adding a perpendicular line BD on side AS makes BDST a rectangle and DADB a right-angle triangle. Since the opposites sides of rectangles are equal, then from BDST we have BT = SD = 4cm If AS = 9cm and SD = 4cm AD = 9-4 = 5cm, AB = 9 + 4 = 13cm In right angle triangle DADB we will calculate the length of BD using Pythagoras theories. $$h_2^2\ =\ 0^2\ +\ a^2$$ $$\left(AB\right)^2\ =\ \left(BD\right)^2\ +\ \left(AD\right)^2$$ Making BD the subject of formula. $$BD\sqrt{\left(AD\right)^2\ -\ \left(AD\right)^2}$$ $$BD\sqrt{\left(13\right)^2\ -\ \left(5\right)^2}$$ $$BD\sqrt{144}=\ 12cm$$ Remember that opposite sides in a rectangle are equal so from rectangle BDST. BT = SD = 4cm BT = ST = 12cm Hence, Statement 1 is SUFFICIENT. $$Statement\ 2\ =\ PB\ =\ \frac{52}{5}cm$$ In right angle triangle BTP we only know the length of PB to find the length of the other sides of this triangle we need to know other length of the other sides of this triangle, we need to know either one of the unknown angles or unknown sides, but we were not given enough information to calculate the distance ST, hence Statement 2 is NOT SUFFICIENT. Option A is CORRECT. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1125 messages Followed by: 29 members Upvotes: 59 AAPL wrote: Source: e-GMAT A bigger circle (with center A) and a smaller (circle with center B) are touching each other externally. PT and PS are tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST? (1) The radii of the bigger and the smaller circles are 9cm and 4cm respectively. (2) PB = 52/5 cm. $? = ST$ (1) Sufficient: $\Delta PTB\,\, \cong \,\,\,\Delta PSA\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered} \,\frac{4}{9} = \,\frac{{4 + {\text{aux}}}}{{9 + 4 + 4 + {\text{aux}}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{aux}}\,\,\,{\text{unique}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,PT\,\,\,{\text{unique}} \hfill \\ \,\frac{9}{4} = \frac{{ST + PT}}{{PT}}\,\,\,\,\,\mathop \Rightarrow \limits^{PT\,\,{\text{unique}}} \,\,\,\,?\,\, = \,\,ST\,\,{\text{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{SUFF}}. \hfill \\ \end{gathered} \right.$ $\left( * \right)\,\,\,\Delta PTB\,\,\,\left\{ \begin{gathered} TB = 4 \hfill \\ \left( {{\text{4}}\,{\text{ + }}\,{\text{aux}}} \right)\,\,{\text{unique}} \hfill \\ \end{gathered} \right.\,\,\,\,\mathop \Rightarrow \limits^{{\text{Pythagoras}}} \,\,\,\,\,PT\,\,\,\,{\text{unique}}$ (2) Insufficient: 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 • FREE GMAT Exam Know how you'd score today for$0

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