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What is the length of AD if the radius of the circle is 6 and the leng

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What is the length of AD if the radius of the circle is 6 and the leng  [#permalink]

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New post 29 Aug 2018, 01:46
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Re: What is the length of AD if the radius of the circle is 6 and the leng  [#permalink]

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New post 29 Aug 2018, 02:03
What is the length of AD if the radius of the circle is 6 and the length of the arc ACB is 4π? (Assume O is the center.)


A. 8
B. 6
C. 5
D. 4
E. 3

from arc ACB we know angle is 120*, so triangle ADO will be equilateral , IMO AD will be 6..
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Re: What is the length of AD if the radius of the circle is 6 and the leng  [#permalink]

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New post 29 Aug 2018, 15:53
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Bunuel wrote:
Image
What is the length of AD if the radius of the circle is 6 and the length of the arc ACB is 4π? (Assume O is the center.)


A. 8
B. 6
C. 5
D. 4
E. 3


Attachment:
image009.jpg


Given, length of arc ACB=4π

Angle subtended by arc ACB at the center of circle, \(\angle{AOB}\) =\(360*(\frac{4π}{4π*6})\)=\(360/3\)=120 degree

We have \(\angle{AOD}+\angle{AOB}=180\)
Or, \angle{AOD}=180-120=60 degree

Now, ADO has \(\angle{AOD}=60\)degree, OA=OD=radius=6 So, \(\angle{OAD}=\angle{ADO}=60.\)
Implies that ADo is an equilateral triangle. hence AD=OA=OD=6

Ans. (B)
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Re: What is the length of AD if the radius of the circle is 6 and the leng   [#permalink] 29 Aug 2018, 15:53
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