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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 ## Is the point Q on the circle with center C ? tagged by: AbeNeedsAnswers ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Is the point Q on the circle with center C ? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is the point Q on the circle with center C ? (1) R is a point on the circle and the distance from Q to R is equal to the distance from Q to C. (2) S is a point on the circle and the distance from Q to S is equal to the distance from S to C. E Source: Official Guide 2020 ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10196 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're asked if the point Q is on the circle with center C. This is a YES/NO question and can be approached with some logic (and a few examples/drawings might help). (1) R is a point on the circle and the distance from Q to R is equal to the distance from Q to C. Since C is the CENTER of the circle, and R is on the circumference, we know that CR is a RADIUS of the circle. With the information in Fact 1, point Q can be ANY point that is equidistance from R and C. IF.... -we have an equilateral triangle, with R and Q on the circumference, then the answer to the question is YES. -we have point Q in the exact middle of the radius CR, then the answer to the question is NO. Fact 1 is INSUFFICIENT (2) S is a point on the circle and the distance from Q to S is equal to the distance from S to C. Since C is the CENTER of the circle, and S is on the circumference, we know that CS is a RADIUS of the circle. With the information in Fact 2, we know that the length of QS is the SAME length as the RADIUS. IF.... -we have an equilateral triangle, with S and Q on the circumference, then the answer to the question is YES. -we have point Q in any other position that is exactly one radius in length from point S, then the answer to the question is NO. Fact 2 is INSUFFICIENT Combined, we know... R is a point on the circle and the distance from Q to R is equal to the distance from Q to C. S is a point on the circle and the distance from Q to S is equal to the distance from S to C. With both Facts, we can create two different examples: -we have two equilateral triangles, with Q on the circumference and R and S on opposite sides of Q, then the answer to the question is YES. -we have an isosceles triangle, with Q OUTSIDE of the circle and CR as the non-equal side, then the answer to the question is NO. Combined, INSUFFICIENT Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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 GMAT Exam Know how you'd score today for$0

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