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

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24 Nov 2017, 00:31
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Difficulty:

25% (medium)

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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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 $$OB - BN = 10 - 2 = 8$$

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Kudos [?]: 3 [0], given: 57

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4485

Kudos [?]: 3172 [0], given: 0

GPA: 3.82
Re: A circle with center (6,8) and radius 2 lies in the standard xy-plane. [#permalink]

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26 Nov 2017, 17:30
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A.png [ 7.44 KiB | Viewed 131 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.

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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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