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Circle K has a total area of 9pi. Circle M has a total area
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30 Sep 2019, 15:36
30 Sep 2019, 15:36
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Circle K has a total area of \(9\pi\). Circle M has a total area of \(49\pi\). Suppose the circles intersect at exactly one point. Which of the following could be the distance from the center for Circle K to the center of Circle M?
A. 8
B. 21
C. 10
D. 29
E. 58
Kudos for the right answer and explanation
A. 8
B. 21
C. 10
D. 29
E. 58
Kudos for the right answer and explanation
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Circle K has a total area of 9pi. Circle M has a total area
[#permalink]
07 Jun 2020, 01:10
07 Jun 2020, 01:10
[Refer attached figure]
image-1.jpg [ 59.97 KiB | Viewed 1064 times ]
Since the two circles are intersecting only at one point then it means that the distance between their centers = sum of their radius
Note that if two circles intersect at more than two points then distance between their centers will be less than sum of their radius
=> Distance from the center for Circle K to the center of Circle M = Radius of Circle K + Radius of Circle M = k + m [where k and m are radius of circle M and K respectively]
Circle K has a total area of \(9\pi\) = \(\pi\)\(k^2\) [We know that area of Circle with radius r is \(9\pi\)]
=> \(k^2\) = 9 => k = 3
Circle M has a total area of \(49\pi\) = \(\pi\)\(m^2\) [We know that area of Circle with radius r is \(9\pi\)]
=> \(m^2\) = 49 => m = 7
Distance from the center for Circle K to the center of Circle M = k + m = 3 + 7 = 10
So, answer will be C
Hope it helps!
Watch the following video to Learn Basics of Circles
Attachment:
image-1.jpg [ 59.97 KiB | Viewed 1064 times ]
Since the two circles are intersecting only at one point then it means that the distance between their centers = sum of their radius
Note that if two circles intersect at more than two points then distance between their centers will be less than sum of their radius
=> Distance from the center for Circle K to the center of Circle M = Radius of Circle K + Radius of Circle M = k + m [where k and m are radius of circle M and K respectively]
Circle K has a total area of \(9\pi\) = \(\pi\)\(k^2\) [We know that area of Circle with radius r is \(9\pi\)]
=> \(k^2\) = 9 => k = 3
Circle M has a total area of \(49\pi\) = \(\pi\)\(m^2\) [We know that area of Circle with radius r is \(9\pi\)]
=> \(m^2\) = 49 => m = 7
Distance from the center for Circle K to the center of Circle M = k + m = 3 + 7 = 10
So, answer will be C
Hope it helps!
Watch the following video to Learn Basics of Circles
gmatclubot
Circle K has a total area of 9pi. Circle M has a total area [#permalink]
07 Jun 2020, 01:10
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