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

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Bunuel
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The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   23 Jun 2020, 06:19
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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 ?

I. 180°
II. 240°
III. 270°

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

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Re: The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   23 Jun 2020, 06:30
D is the answer. The angle must be greater than 180 degree.

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The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   23 Jun 2020, 06:32
Length of arc ABC > 26

Length of arc = Π/360*2πr
Where Π is the sum of angle of AQB and BQC

Let length of arc be 26.1
Therefore,
27 = Π/360*2*22/7*8
Π = 186.85 or 187° is the least sum of angle AQB and BQC

Therefore The sum of AQB+BQC satisfy all two values of B and C

IMO D

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Re: The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   23 Jun 2020, 22:18
@yashikaagggarwal : can you please explain

27 = Π/360*2*22/7*8... what does the *2 signify ? where did you get the *2 from?
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Re: The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   23 Jun 2020, 22:26
VERBAL1 wrote:
@yashikaagggarwal : can you please explain

27 = Π/360*2*22/7*8... what does the *2 signify ? where did you get the *2 from?


In (Π/360)*2*22/7*8
Π is the angle, AQC
2*22/7*8 = circumference formula.
Which is in multiplication, to get the value of arc we multiply theta/360 to circumference to draw out value of the arc.

Hope that helps

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The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   23 Jun 2020, 22:30
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Bunuel wrote:

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 ?

I. 180°
II. 240°
III. 270°

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Show Spoiler
Attachment:
1.jpg


ANgle AQB + Angle BQC = Angle AQC

Angle AQC is drawn by arc ABC at the center

Length of Arc \(= (\frac{ø}{360})*2πr\)

ie. Length of Arc ABC \(= (\frac{ø}{360})*2π*8\) > 26 (Given)

i.e. \(= (\frac{ø}{360})*2π*8 > 26\)

i.e. Angle (ø) > 186º



I. 180°
II. 240°
III. 270°

Answer: Option D

VERBAL1
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Re: The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   23 Jun 2020, 23:06
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Circumference of the circle (radius =8) =\( 2 \pi r = 2*3.14*8 \approx48\)
So semi-circumference (or arc subtended by the diameter) \(\approx24\) <26
Angle at the centre of the sem-circumference = \(180^{\circ}\)
So the angle must be greater than \(180^{\circ}\)
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Re: The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink] New post   20 Mar 2023, 12:25
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Re: The radius of Circle Q is 8. If the length of arc ABC is greater than [#permalink]
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