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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: 50623
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, 00:46
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:57) correct 6% (01:54) wrong based on 31 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 359 times ]

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Joined: 18 Aug 2017
Posts: 215
Concentration: Healthcare, Marketing
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, 01:03
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..
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)
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, 14:53
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, $$\angle{OAD}=\angle{ADO}=60.$$

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, 14:53
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