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A is the center of the circle above.
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07 Feb 2023, 02:31
07 Feb 2023, 02:31
Expert Reply
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Question Stats:
61% (01:49) correct
38% (02:10) wrong based on 73 sessions
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A is the center of the circle above.
Quantity A |
Quantity B |
The perimeter of triangle ABC |
The perimeter of the shaded region |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: A is the center of the circle above.
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20 Feb 2023, 07:43
20 Feb 2023, 07:43
1
Expert Reply
OE
The two perimeters share the line BC, therefore, you can recast this question:
A. The combined length of two radii (AB and AC)
B. The length of arc BDC
The easiest thing to do in this situation is use numbers. Assume the radius of the circle is 2. If the radius is 2, then you can rewrite Quantity A is 4
Now you need to figure out the length of arc BDC if the radius is 2. You can set up a proportion, because the ratio of central angle to 360° will be the same as the ratio of the arc length to the circumference:
120/360=1/3
Circumference is \(2 \pi r\)
\(C=2 \pi (2) = 4 \pi\)
Arc length is 1/3 so it is \(\frac{4 \pi}{3}\)
So B >A
The two perimeters share the line BC, therefore, you can recast this question:
A. The combined length of two radii (AB and AC)
B. The length of arc BDC
The easiest thing to do in this situation is use numbers. Assume the radius of the circle is 2. If the radius is 2, then you can rewrite Quantity A is 4
Now you need to figure out the length of arc BDC if the radius is 2. You can set up a proportion, because the ratio of central angle to 360° will be the same as the ratio of the arc length to the circumference:
120/360=1/3
Circumference is \(2 \pi r\)
\(C=2 \pi (2) = 4 \pi\)
Arc length is 1/3 so it is \(\frac{4 \pi}{3}\)
So B >A
Re: A is the center of the circle above.
[#permalink]
26 Jan 2026, 17:14
26 Jan 2026, 17:14
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