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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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Math Expert
Joined: 02 Sep 2009
Posts: 49252
What is the length of AD if the radius of the circle is 6 and the leng  [#permalink]

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29 Aug 2018, 01:46
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Difficulty:

15% (low)

Question Stats:

93% (02:01) correct 7% (01:54) wrong based on 27 sessions

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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 [ 2.42 KiB | Viewed 306 times ]

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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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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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Joined: 01 Oct 2017
Posts: 848
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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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29 Aug 2018, 15:53
1
Bunuel wrote:

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 &nbs [#permalink] 29 Aug 2018, 15:53
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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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