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505-555 (Easy)|   Geometry|      
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enigma123
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If equilateral triangle MNP is inscribed in circle O with 31 Mar 2012, 16:46
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79% (01:27) correct 21% (01:43) wrong based on 127 sessions

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If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?

(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?
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B
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Bunuel
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If equilateral triangle MNP is inscribed in circle O with 31 Mar 2012, 16:52
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enigma123
If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?
(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?
Show more

Since triangle MNP is equilateral each of the 3 minor arcs (MN, NP, PM) will equal to 1/3rd of the circumference, which is \(2\pi{r}=12\pi\). Hence, the length of minor arc MN is \(\frac{12\pi}{3}=4\pi\).

Answer: B.
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If equilateral triangle MNP is inscribed in circle O with 01 Apr 2012, 15:18
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Bunuel
enigma123
If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?
(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?

Since triangle MNP is equilateral each of the 3 minor arcs (MN, NP, PM) will equal to 1/3rd of the circumference, which is \(2\pi{r}=12\pi\). Hence, the length of minor arc MN is \(\frac{12\pi}{3}=4\pi\).

Answer: B.
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I understand the answer, but was initially thrown off by calculating that each triangle angles is 60 degrees and circumference is 12 pi so 60/360 * 12pi = 2pi. What's wrong with this reasoning? Thank you.
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If equilateral triangle MNP is inscribed in circle O with 01 Apr 2012, 16:12
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bohdan01
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enigma123
If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?
(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?

Since triangle MNP is equilateral each of the 3 minor arcs (MN, NP, PM) will equal to 1/3rd of the circumference, which is \(2\pi{r}=12\pi\). Hence, the length of minor arc MN is \(\frac{12\pi}{3}=4\pi\).

Answer: B.

I understand the answer, but was initially thrown off by calculating that each triangle angles is 60 degrees and circumference is 12 pi so 60/360 * 12pi = 2pi. What's wrong with this reasoning? Thank you.
Show more

The angle in the formula you are using should be a central angle and 60 degrees angle is inscribed angle.

Now, according to the central angle theorem the measure of inscribed angle is always half the measure of the central angle.. So, the corresponding central angles would be 2*60=120 degrees and if we put this value in your formula we'll get 120/360*12pi=4pi, which is a correct answer.

For more on this subject check Circles chapter of Math Book: math-circles-87957.html

Hope it helps..
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If equilateral triangle MNP is inscribed in circle O with 04 Jun 2020, 06:14
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