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# The center is at point (0,6). The distance between the two

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CEO
Joined: 21 Jan 2007
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The center is at point (0,6). The distance between the two [#permalink]  23 Oct 2007, 12:37
The center is at point (0,6). The distance between the two points where the circle intersects the x-axis is 16. What is the area of the circle?

36 pi
45 pi
64 pi
81 pi
100 pi
Intern
Joined: 16 Oct 2007
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Re: Challenge - Area of a Circle [#permalink]  23 Oct 2007, 12:52
draw a diagram it will be clear we get a rt angle, height 6 base 8 hypotenuse i.e circle radius = 10.

bmwhype2 wrote:
The center is at point (0,6). The distance between the two points where the circle intersects the x-axis is 16. What is the area of the circle?

36 pi
45 pi
64 pi
81 pi
100 pi
Senior Manager
Joined: 06 Mar 2006
Posts: 497
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Kudos [?]: 91 [0], given: 1

Consider that as a special right triangle. The radius of this circle will be the hypotenus ( I hope I spelled correctly.) of this right triangle. Since the center of the circle is (0,6) so the distance from the center of the circle to the origin will be 6. And since the distance for the intersection of x-axis is 16. This will be a bisect. and the distance from the original to one of the point of x-axis intersection will be 8. So this is a 6-8-10 special triangle. Therefore, the radius is 10 and the area of this circle will be 100pi, or answer E
CEO
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can someone draw it out for me? it is not clear to me at all.

we have a point at (0,6) and it hits the x axis at (0,0) . where are u getting the triangle from?
Director
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See attached,
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circle_gmat.jpg [ 8.27 KiB | Viewed 564 times ]

Manager
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Late, but 100*Pi

We have equilateral triangle which consists of two right 3-4-5 triangles with the sides 6-8-10

S = Pi * 10^2 = 100*Pi
Director
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Re: Challenge - Area of a Circle [#permalink]  21 Dec 2007, 20:58
bmwhype2 wrote:
The center is at point (0,6). The distance between the two points where the circle intersects the x-axis is 16. What is the area of the circle?

36 pi
45 pi
64 pi
81 pi
100 pi

As the center of the circle is (0,6), on Y-axis, and the circle intersects the X-axis at two points, which means on the positive side of the axis as well as on the negative side of the axis. Thus distance from the center of the circle to the point of intersection will be radius.
and points on X axis will be ( -8,0 ) and ( +8, 0)

6 is the distance from origin to the center,

8 is the distance from origin to the point of intersection

Therefore r^2 = 6^2 + 8^2

r=10

Area = 100pi
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
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Kudos [?]: 349 [0], given: 4

Re: Challenge - Area of a Circle [#permalink]  21 Dec 2007, 23:34
LM wrote:
bmwhype2 wrote:
The center is at point (0,6). The distance between the two points where the circle intersects the x-axis is 16. What is the area of the circle?

36 pi
45 pi
64 pi
81 pi
100 pi

As the center of the circle is (0,6), on Y-axis, and the circle intersects the X-axis at two points, which means on the positive side of the axis as well as on the negative side of the axis. Thus distance from the center of the circle to the point of intersection will be radius.
and points on X axis will be ( -8,0 ) and ( +8, 0)

6 is the distance from origin to the center,

8 is the distance from origin to the point of intersection

Therefore r^2 = 6^2 + 8^2

r=10

Area = 100pi

thanks for clarifying

OA is 100pi
Re: Challenge - Area of a Circle   [#permalink] 21 Dec 2007, 23:34
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