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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 If O is the center of the circle with diameter AB and T is a tagged by: fskilnik@GMATH This topic has 4 expert replies and 0 member replies GMAT/MBA Expert If O is the center of the circle with diameter AB and T is a Timer 00:00 Your Answer A B C D E Global Stats Difficult GMATH practice exercise (Quant Class 7) If O is the center of the circle with diameter AB and T is a tangency point, what is the value of x? (A) 10 (B) 15 (C) 18 (D) 20 (E) 22.5 Answer: ____(C)__ _________________ 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 08 Dec 2008 Posted: 13001 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 7) If O is the center of the circle with diameter AB and T is a tangency point, what is the value of x? (A) 10 (B) 15 (C) 18 (D) 20 (E) 22.5 Answer: ____(C)__ Since angles in a triangle add to 180Â°, we know that the missing angle = (90 - 2x)Â° Aside: Notice that (90 - 2x)Â° + 90Â° + 2xÂ° =180Â° Since angles on a line add to 180Â°, we know that the missing angle = (90 + 2x)Â° Aside: Notice that (90 - 2x)Â° + (90Â° + 2xÂ°) =180Â° Next, draw a line from the center to the point of tangency. One of our circle properties tells us that this line is PERPENDICULAR to the tangent line. Now focus on âˆ†ATO (below) Since OT and OA are radii, we know that OT = OA, which makes âˆ†ATO an ISOSCELES triangle. This means the other angle is ALSO (90 - 2x)Â° Next, since OT is PERPENDICULAR to the tangent line, the remaining angle must be 2xÂ° Aside: Notice that (90 - 2x)Â° + 2xÂ° =90Â° Finally, we'll focus on the green triangle. Since angles in a triangle add to 180Â°, we can write: xÂ° + 2xÂ° + (90 + 2x)Â° = 180Â° Simplify: 5xÂ° + 90Â° = 180Â° Solve to get: x = 18 Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! 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) If O is the center of the circle with diameter AB and T is a tangency point, what is the value of x? (A) 10 (B) 15 (C) 18 (D) 20 (E) 22.5 Post appeared twice. Please see my solution below! _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Last edited by fskilnik@GMATH on Tue Feb 12, 2019 4:50 am; edited 1 time in total 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) If O is the center of the circle with diameter AB and T is a tangency point, what is the value of x? (A) 10 (B) 15 (C) 18 (D) 20 (E) 22.5 Hi, Brent! Thank you for your nice contribution and beautiful drawings! Alternate approach: (Click in the figure to "zoom" it! All angles are measured in degrees.) $$? = x$$ $$\Delta BTC\,\,:\,\,\,3x + 2x = 90\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {{90} \over 5} = 18$$ The correct answer is (C). 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 GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 7) If O is the center of the circle with diameter AB and T is a tangency point, what is the value of x? (A) 10 (B) 15 (C) 18 (D) 20 (E) 22.5 A radius drawn to a tangent point yields a RIGHT ANGLE: In the figure above: Radius OT forms a right angle at tangent point T. OA and OT are radii and thus are equal. Since OA=OT, opposite angles OAT and ATO are equal. We can PLUG IN THE ANSWERS, which represent the value of x. From left to right, option D yields the following 3 triangles: In this case, the resulting angle sum for the green triangle is TOO BIG: 20+80+90 = 190. Eliminate D. From left to right, option B yields the following 3 triangles: In this case, the resulting angle sum for the green triangle is TOO SMALL: 15+60+90 = 165. Eliminate B. Since D yields a sum that is TOO BIG, while B yields a sum that is TOO SMALL, the correct answer must be BETWEEN B AND D. The correct answer is C. _________________ 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. 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