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Length of an arc

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Director
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Joined: 25 Oct 2008
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Location: Kolkata,India
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Length of an arc [#permalink] New post 13 Sep 2009, 21:14
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (03:38) wrong based on 1 sessions
AE // BD. AD is also the diameter.If the length of arc BCD is 4pi then what is the area of the circle??

My method:
Join BA. Angle ABD is 90deg. Therefore BAD =60
Now, the formula is:
Length of an arc= circumference x angle presented by the arc/360
Hence, 4pi=2.pi.r.60/360
r=12
Area=144pi.

Now could somebody please point out where I am going wrong?
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Re: Length of an arc [#permalink] New post 13 Sep 2009, 21:36
So I think you got the length of the arc formula wrong :

Length of Arc = C/360 (2 * 22/7 * r )
where C is the angle subtended by the arc in the centre

So join BE to intersect the diameter at center O. Now I don't how to find out angle BOD. But once you get that you have your answer.
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Re: Length of an arc [#permalink] New post 13 Sep 2009, 22:00
- Draw a line from B to O (circle centre)
- BO = OD (both radii) and now ODB is iscoceles triangle
- EAD = ADB = DBO = 30 degrees
- angle of arc at centre = 120 degrees (180-30-30)

So 120/360 (2* Pi * r) = 4 * Pi
solving you get r = 6
Area = 36 Pi
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Re: Length of an arc [#permalink] New post 14 Sep 2009, 05:50
yangsta8 wrote:
- Draw a line from B to O (circle centre)
- BO = OD (both radii) and now ODB is iscoceles triangle
- EAD = ADB = DBO = 30 degrees
- angle of arc at centre = 120 degrees (180-30-30)

So 120/360 (2* Pi * r) = 4 * Pi
solving you get r = 6
Area = 36 Pi


thats one way of solving it ....u can also solve this by using the "angle at center theorm".....ie

the angle subtended by the arc at the center is twice the angle subtended by it at any other point on the circle.

arc BCD makes angle 60 deg at a : angle BAD = 60. therefore the angle made by the same arc at center :ang BOD = 120 deg.

so using ur formula....4 pi = 2pi *r* *[120/306]
r = 6
area = pi*r*r
= 36pi.

:-D
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Re: Length of an arc [#permalink] New post 14 Sep 2009, 08:42
Thanks guys - both the methods are very quick ways of solving this problem.
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Re: Length of an arc   [#permalink] 14 Sep 2009, 08:42
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