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# A circle with center (6,8) and radius 2 lies in the standard xy-plane.

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5836
GMAT 1: 760 Q51 V42
GPA: 3.82
A circle with center (6,8) and radius 2 lies in the standard xy-plane. [#permalink]

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24 Nov 2017, 01:31
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Difficulty:

25% (medium)

Question Stats:

73% (01:00) correct 28% (00:53) wrong based on 40 sessions

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[GMAT math practice question]

A circle with center (6,8) and radius 2 lies in the standard xy-plane. What is the shortest distance between the origin and the points of the circle?

A. 4
B. 6
C. 8
D. 10
E. 12

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 16 Oct 2017 Posts: 30 Location: Ireland Concentration: Healthcare, Finance Re: A circle with center (6,8) and radius 2 lies in the standard xy-plane. [#permalink] ### Show Tags 24 Nov 2017, 06:03 1 MathRevolution wrote: [GMAT math practice question] A circle with center (6,8) and radius 2 lies in the standard xy-plane. What is the shortest distance between the origin and the points of the circle? A. 4 B. 6 C. 8 D. 10 E. 12 If we draw a circle on xy plane and connect its radii with the dash lines, it will form a rectangle with sides 6 and 8 respectively. The rectangle's diagonal is equal to 10 (using Pythagorean theorem $$OB^2 = AO^2 + OC^2 = 8^2 + 6^2 = 100$$ ; $$OB = 10$$) The origin of xy plane is O and we are looking for the length of ON (because it is a shortest distance) so that is egual to $$OB - BN = 10 - 2 = 8$$ Hence, the answer is C Attachments File comment: xy plane and its origin (0;0) xy plane.jpg [ 26.97 KiB | Viewed 394 times ] Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5836 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A circle with center (6,8) and radius 2 lies in the standard xy-plane. [#permalink] ### Show Tags 26 Nov 2017, 18:30 1 Attachment: A.png [ 7.44 KiB | Viewed 317 times ] The distance between the origin and the center of the circle is $$10=\sqrt{6^2+4^2}$$. Since the radius of the circle is $$2$$, the point of the circle closest to the origin lies along the line joining the center to the origin, and so has distance $$10 – 2 = 8$$ from the origin. Therefore, the answer is C. Answer : C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: A circle with center (6,8) and radius 2 lies in the standard xy-plane.   [#permalink] 26 Nov 2017, 18:30
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