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

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New post 24 Nov 2017, 00:31
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Question Stats:

75% (00:53) correct 25% (00:54) wrong based on 32 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
[Reveal] Spoiler: OA

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

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New post 24 Nov 2017, 05:03
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
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Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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Re: A circle with center (6,8) and radius 2 lies in the standard xy-plane. [#permalink]

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New post 26 Nov 2017, 17:30
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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
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Re: A circle with center (6,8) and radius 2 lies in the standard xy-plane.   [#permalink] 26 Nov 2017, 17:30
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