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24 Nov 2017, 01:31
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (01:42) correct
25%
(01:52)
wrong
based on 102
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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
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
24 Nov 2017, 06:03
Kudos
Bookmarks
MathRevolution
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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xy plane.jpg [ 26.97 KiB | Viewed 3067 times ]
26 Nov 2017, 18:30
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Attachment:
A.png [ 7.44 KiB | Viewed 2983 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
