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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 AB and CD are two diameters of circle. ##### This topic has 3 expert replies and 1 member reply ### Top Member ## In the figure AB and CD are two diameters of circle. ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB A. 114 B. 100 C. 80 D. 96 E. 40 OA A Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 964 messages Followed by: 27 members Upvotes: 59 BTGmoderatorDC wrote: In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB A. 114 B. 100 C. 80 D. 96 E. 40 Source: GMAT Prep All angles are measured in degrees. $$? = x = \angle CEB$$ 01. Triangle AOC is isosceles with base AC, hence the 66-degrees angle is justified. 02. Angle BAC is inscribed in the circle, hence the 132-degrees red arc (CEB) is justified. 03. Angle x (our FOCUS) is inscribed in the circle and corresponds to the blue arc CADB, hence: $$? = {{360 - 132} \over 2} = 114\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( A \right)$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12412 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB A. 114 B. 100 C. 80 D. 96 E. 40 OA A Source: GMAT Prep Let's use some useful circle properties First let's add a blue line, to divide âˆ CEB into 2 angles CD is the DIAMETER of the circle Since âˆ CED is an inscribed angle containing (aka "holding") the diameter, we can conclude that âˆ CED = 90Â° Now recognize that the intersection of AB and CD creates two equal (vertically opposite) angles, we can conclude the angle opposite the 48Â° is also 48Â° Now recognize that we have two angles containing (aka "holding") the arc BD Property: If a CENTRAL angle and an INSCRIBED angle contain the same arc, then the CENTRAL angle is TWICE the INSCRIBED angle This means that âˆ DEB = 24Â° At this point, we have: So, âˆ CEB = 90Â° + 24Â° = 114Â° Answer: A RELATED VIDEO https://www.youtube.com/watch?v=xiyv2MacIUk _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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! ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 677 messages Followed by: 4 members Join segment AE in the figure, we know angle AEC is half of angle COA (assuming diameter intersect at point O). Angle AEC = 24. Ab is the diameter, so angle AEB = 90. Angle CEB = 90 + 24 = 114. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14922 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB A. 114 B. 100 C. 80 D. 96 E. 40 An INSCRIBED ANGLE is formed by two chords. A CENTRAL ANGLE is formed by two radii. When an inscribed angle and a central angle intercept the same two points on a circle, the inscribed angle is 1/2 the central angle. Here, inscribed angle CFB and central angle COB both intercept the circle at points C and B. Since central angle COB = 132Âº, inscribed angle CFB = (1/2)(132) = 66Âº. Rule: When a quadrilateral is inscribed in a circle, opposite angles sum to 180Âº. Since opposite angles inside inscribed quadrilateral CEBF must sum to 180Âº, angle CEB = 180-66 = 114. The correct answer is A. _________________ 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. • Award-winning private GMAT tutoring Register now and save up to$200

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