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Area

by sampath » Tue Jul 05, 2011 10:45 pm
The center of the circle is at point (0,6). If the distance between the two points
where the circle intersects the x-axis is 16, what is the area of the circle?

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by edvhou812 » Tue Jul 05, 2011 10:56 pm
Is it 36pie? I'm thinking that the radius must be 6 since the center is six points up the y-axis, but that sounds too simple.

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by sampath » Tue Jul 05, 2011 11:13 pm
I don't think the answer is 36pi it is only the centre. To find the area , we have to determine the radius, which according to the Q stem can be derived from the two points at which the circle intersects at x axis, say (x,0) and (-x,0). The distance given between the two points is 16,
sqrt((2x)^2)=16 ===>x=2 or -2
Therefore, the two points are (2,0) and (-2,0). The radius will be then distance between (0,6)and (2,0)
or (0,6) and (-2,0) which gives sqrt(40). The area will then be 40pi.

But I am not sure whether this is the correct answer or the way to derive it. Need confirmation. Thanks.

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by sampath » Thu Jul 07, 2011 2:05 am
Could someone please help confirm the answer. Thanks.

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by shovan85 » Thu Jul 07, 2011 4:21 am
The center is at (0,6). The circle formed around this center has to be symmetrical against the Y-axis.

The distance between the two points intersecting X-axis is 16. So, we can say the length of the chord is 16.

The distance of any of the points from origin (0,0) is 8 as the circle is symmetric on Y-axis. (i.e the two intersecting points are (8,0) and (-8,0))

Now the radius = sqrt(6^2 + 8^2) = 10

Thus, the area = 100 * pie
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by mayank82 » Thu Jul 07, 2011 6:55 am
if you draw a triangle using center O and two points of intersection call it A and B.
then you get a isoceles triangle since both OA and OB are radius so OA=OB.
And since center is 0,6 which means - Y axis divides AB symterically at 90 degress using pythagorous theorum (hyp) OA=sqrt(6^2 + 8^2) = 10

Area= Pie *10^2=100pie

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by winniethepooh » Thu Jul 07, 2011 9:23 am
@ sampath, why is the answer not 16 pie?
whats the OA?

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by mayank82 » Thu Jul 07, 2011 4:58 pm
@wtp: A and B are two points where circle intersects with x axis and since they are at the circumfrence of the circle and O is the center then OA = OB = radius of the circle.

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by amit2k9 » Thu Jul 07, 2011 11:41 pm
doing a bit of construction we have triangles with 6,8 and r as sides.

thus r=10 hence A = pi* 100.
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by worldpeace93 » Fri Jul 08, 2011 1:57 am
Image

SO answer comes to 292pi.

Can somebody verify this Please?

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by Frankenstein » Fri Jul 08, 2011 2:03 am
worldpeace93 wrote:Image

SO answer comes to 292pi.

Can somebody verify this Please?
Hi,
You are calculating r^2 = 6^2 + 16^2 instead of r^2 = 6^2 + 8^2.
Cheers!

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by shovan85 » Fri Jul 08, 2011 2:14 am
worldpeace93 wrote:Image

SO answer comes to 292pi.

Can somebody verify this Please?
Image
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