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# If the length of AB is 12 and the radius of the circle is , what is th

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Math Expert
Joined: 02 Sep 2009
Posts: 55231
If the length of AB is 12 and the radius of the circle is , what is th  [#permalink]

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14 Sep 2018, 02:17
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75% (hard)

Question Stats:

41% (03:20) correct 59% (02:31) wrong based on 23 sessions

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If the length of AB is 12 and the radius of the circle is $$6\sqrt{3}$$, what is the length of the arc ACB?

A. 24π
B. 18π
C. 16π
D. 12π
E. 8π

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Math Expert
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Posts: 7684
If the length of AB is 12 and the radius of the circle is , what is th  [#permalink]

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14 Sep 2018, 04:56
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Bunuel wrote:

If the length of AB is 12 and the radius of the circle is $$6\sqrt{3}$$, what is the length of the arc ACB?

A. 24π
B. 18π
C. 16π
D. 12π
E. 8π

Attachment:
image039.jpg

rahulkashyap
We are not required to know trigonometry, so there must be some other way..
Circumference =2π*6√3=12π√3=20.8π
So the size of a minor arc can at the max be closer to half circle ~10.4π
But here we are talking of a chord of 12 where the diameter is 12√3π

Only E is possible

But it will not be 6√2 because then the triangle being formed by the centre and the endpoint of chord AB will be isosceles right angled triangle with sides 6√2:6√2:12
Ratio of 1:1:√2 thus 45:45:90

Then arc ACB will be 2πr*90/360=π*6√2*1/2=3√2π
Not in the choices, so radius cannot be 6√2
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Re: If the length of AB is 12 and the radius of the circle is , what is th  [#permalink]

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14 Sep 2018, 02:35
1
chetan2u, assuming we have the missing number for this diameter, what exactly would be the theory behind the working? would we have to use parallel lines for this?
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Posts: 55231
Re: If the length of AB is 12 and the radius of the circle is , what is th  [#permalink]

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14 Sep 2018, 02:37
rahulkashyap wrote:
chetan2u, assuming we have the missing number for this diameter, what exactly would be the theory behind the working? would we have to use parallel lines for this?

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Edited. Thank you.
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Re: If the length of AB is 12 and the radius of the circle is , what is th  [#permalink]

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14 Sep 2018, 02:52
using similar triangles, we get that AB can be split into two halves, 6 and 6

with the radius as 6 root 3 and the one half of the chord as 6, we get the height of the triangle formed as 6 root 2.
However, from this i am unable to calculate the angle of the triangle, needed to calculate the length of the arc.
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If the length of AB is 12 and the radius of the circle is , what is th  [#permalink]

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14 Sep 2018, 03:01
Bunuel wrote:
rahulkashyap wrote:
chetan2u, assuming we have the missing number for this diameter, what exactly would be the theory behind the working? would we have to use parallel lines for this?

________________
Edited. Thank you.

Hi Bunuel is the radius $$6 \sqrt{2}$$ or $$6 \sqrt{3}$$? because with the given radius, that is $$6 \sqrt{3}$$, i am unable to calculate the angle using trig
chetan2u
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If the length of AB is 12 and the radius of the circle is , what is th  [#permalink]

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14 Sep 2018, 11:21
what is the length of the arc ACB?

A. 24π
B. 18π
C. 16π
D. 12π
E. 8π

I solve this one with POE, the diameter of the circle is 12 root 3, and AB is 12, that means that the arc acb has to be smaller then the semicircle arc, because the diameter is the largest line segment in circle,if we move either way the value of the segment will get smaller.

now the total circmfrnc is 2pir= 2*pi*6root3=12root3*pi.then we will only be left with option E.
If the length of AB is 12 and the radius of the circle is , what is th   [#permalink] 14 Sep 2018, 11:21
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