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07 Sep 2015, 22:58
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:
45%
(medium)
Question Stats:
69% (02:15) correct
31%
(02:05)
wrong
based on 156
sessions
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In the figure above, angles BAD and BCD each equal 120°, points A and C are the centers of their respective circles and are points on the opposite circles, and line segment AC = 3. What is the perimeter of the exterior of the figure, without any of the lines within?
(A) 16π
(B) 12π
(C) 8π
(D) 4π
(E) It cannot be determined from the information given.
Kudos for a correct solution.
Attachment:
circles.gif [ 4.64 KiB | Viewed 4786 times ]
08 Sep 2015, 01:14
Kudos
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Hi,
The answer is C :8π
Now, AC=AB=BC=3 (radius of the circle).
Hence each angle BAC=ACB=CBA=60°
Hence perimeter of arc along BC = (60/360)*2π*3 = π. We have 4 such perimeters. = 4π
Total perimeter = 2πr = 12π
Required perimeter = 12π - 4π = 8π
Regards,
Dom.
The answer is C :8π
Now, AC=AB=BC=3 (radius of the circle).
Hence each angle BAC=ACB=CBA=60°
Hence perimeter of arc along BC = (60/360)*2π*3 = π. We have 4 such perimeters. = 4π
Total perimeter = 2πr = 12π
Required perimeter = 12π - 4π = 8π
Regards,
Dom.
08 Sep 2015, 04:55
Kudos
Bookmarks
Solution:
Length of an arc made by radii(r) with an angle A at the center is Ar.
So, length of arc BAD = length of arc BCD = (2π/3)*3 = 2π
Required length = 2(2πr-2π) = 2(6π-2π) =8π
Option C
Length of an arc made by radii(r) with an angle A at the center is Ar.
So, length of arc BAD = length of arc BCD = (2π/3)*3 = 2π
Required length = 2(2πr-2π) = 2(6π-2π) =8π
Option C
