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In the above circle, the radius is 6 and chord AB = 6. What is the are

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In the above circle, the radius is 6 and chord AB = 6. What is the are  [#permalink]

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07 May 2011, 07:58
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In the above circle, the radius is 6 and chord AB = 6. What is the area of the shaded region?
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Re: In the above circle, the radius is 6 and chord AB = 6. What is the are  [#permalink]

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07 May 2011, 08:32
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Joint the ends of the chord with the center of the circle. You will get an equilateral triangle.

So the required area = area of sector with angle 60 - area of equilateral triangle.

= $$\frac{60}{360} * pie * 6* 6 -$$ $${\sqrt{3}}$$$$/4 *6*6$$

= $$6*pie - \sqrt{3}*9$$
Hence E
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Re: In the above circle, the radius is 6 and chord AB = 6. What is the are  [#permalink]

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07 May 2011, 09:36
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From A and B draw line segments to the center of the circle O

triangle ABC is equilateral triangle sides 6,6,6. Hence angel at the center angel AOB = 60 deg

area of sector = (60/360) pi 36 = 9pi

area of equilateral triangle = (3^2/4) (side)^2 = 6* 3^(1/2)

hence difference between area of sector and area of triangle = 6* 3^(1/2) - 9pi.

Is the solution.
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Re: In the above circle, the radius is 6 and chord AB = 6. What is the are  [#permalink]

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08 May 2011, 08:19
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Area = pi * (6)^2/6 - root(3)/4 * 36

= 6pi - 9root(3)

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Re: In the above circle, the radius is 6 and chord AB = 6. What is the are  [#permalink]

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04 Aug 2018, 21:03
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Re: In the above circle, the radius is 6 and chord AB = 6. What is the are &nbs [#permalink] 04 Aug 2018, 21:03
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