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The radius of Circle Q is 8. If length of arc ABC is greater

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The radius of Circle Q is 8. If length of arc ABC is greater [#permalink] New post 24 Feb 2020, 15:05
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The radius of Circle Q is 8. If the length of arc ABC is greater than 26, which of the following could be the value of the sums of angles AQB and BQC ?

Indicate all such values.

A. 45°

B. 60°

C. 90°

D. 150°

E. 180°

F. 240°

G. 270°


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[Reveal] Spoiler: OA

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Re: The radius of Circle Q is 8. If length of arc ABC is greater [#permalink] New post 24 Feb 2020, 23:59
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this is the explanation.
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Re: The radius of Circle Q is 8. If length of arc ABC is greater [#permalink] New post 25 Feb 2020, 11:41
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I appreciate a lot your effort Sir.

However, the question should be written as a reply. The images do not help that much.,

Also they are not reported on google.

Regards
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Re: The radius of Circle Q is 8. If length of arc ABC is greater [#permalink] New post 05 Mar 2020, 17:33
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# Length of arc in circle = circumference of circle * (center angle/ 360)
center angle(here) = <AQB +<BQC
SO, sum of center angle= (length of arc * 360)/ 2 * 3.14 * 8, where radius =8 and length of arc = 26 is given..
=(26*360)/2*3.14*8
=186.305
Therefore, sum of center angle must be greater than 186.305..
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Re: The radius of Circle Q is 8. If length of arc ABC is greater [#permalink] New post 04 May 2020, 04:16
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Redius=8 So circumference =2*3.14*8=50.24
from the question we know that arc ABC is greater than 26 ( which means more than half of circle ), so the angle of arc ABC is also greater than half of the angle of circle (>180)

So , F and G are right answers
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Re: The radius of Circle Q is 8. If length of arc ABC is greater [#permalink] New post 13 Jun 2020, 14:08
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Arc length of a sector = angle/360 * (2*pi*r)
For AQB: Arc=angle1/360*(2*pi*8)
=angle1/360 * (16pi)
Same for BQC: angle2/360 * (16pi)

Now, Sum both values: angle1/360 * 16pi + angle2/360 * 16 pi
take common: angle1 + angle2 (16pi/360)
given that arc is greater than 26 so,
(16pi/360) angle1 + angle2 >26
angle1 + angle2 > (26 * 360) / 16 pi
=186.3
Hence sum of angles would be greater than this value so option F and G
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Re: The radius of Circle Q is 8. If length of arc ABC is greater   [#permalink] 13 Jun 2020, 14:08
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