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# Equilateral triangle is inscribed in a circle. If length of arc ABC is

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Manager
Joined: 10 Feb 2011
Posts: 104
Equilateral triangle is inscribed in a circle. If length of arc ABC is  [#permalink]

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Updated on: 14 Oct 2018, 06:26
2
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Difficulty:

75% (hard)

Question Stats:

66% (01:22) correct 34% (01:46) wrong based on 75 sessions

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Equilateral triangle is inscribed in a circle. If length of arc ABC is 2pi, what is the radius of the circle?

(A) 1
(B) 3/2
(C) 2
(D) 5/3
(E) 3

Originally posted by banksy on 05 Mar 2011, 08:50.
Last edited by generis on 14 Oct 2018, 06:26, edited 1 time in total.
Edited the OA
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: Equilateral triangle is inscribed in a circle. If length of arc ABC is  [#permalink]

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05 Mar 2011, 09:16
banksy wrote:
164 Equilateral triangle is inscribed in a circle. If length of arc ABC is 2pi, what is the radius of the circle?
(A) 1
(B) 3/2
(C) 2
(D) 5/3
(E) 3

Arc ABC is $$\frac{2}{3}$$ of the circumference (as ABC is equilateral triangle then (arc AB)=(arc BC)=(arc AC), so (arc AB)+(arc BC)=(arc ABC)=2/3 of circumference, so $$arc \ ABC=2\pi$$ basically means that the circumference is $$3\pi$$ --> $$circumference=2\pi{r}=3\pi$$ --> $$r=\frac{3}{2}$$.

Similar question: geometry-circle-triangle-from-mba-com-97393.html
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Re: Equilateral triangle is inscribed in a circle. If length of arc ABC is  [#permalink]

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Updated on: 05 Mar 2011, 09:51
Yep, thanks Bunuel.
But I don't understand why it is not possible to use another method to solve it....
it drives me crazy cos I don't understand what is wrong with it...please look..

I used formula:
Circumference of sector= (angle in front of the sector/ 360) * 2*pi*R

so if we know that ABC equilateral, so all angles=60 and all circumferences in front of A ,B and C are same. so if circumference in front of 2 angles = 2pi, so circumference in front of one angle is pi.
so
pi= 60/360*2pi*R
so pi=1/6*2pi*R
so pi=1/3pi*R
R=3....

i hope it is clear what I wrote here.
so what is wrong with it?

Originally posted by banksy on 05 Mar 2011, 09:28.
Last edited by banksy on 05 Mar 2011, 09:51, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 58335
Re: Equilateral triangle is inscribed in a circle. If length of arc ABC is  [#permalink]

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05 Mar 2011, 09:37
1
banksy wrote:
Yep, thanks Bunuel.
But I don't understand why it is not possible to use another method to solve it....
it drives me crazy cos I don't understand what is wrong with it...please look..

I used formula:
Circumference of sector= (angle in front of the sector/ 360) * 2*pi*R

so if we know that ABC equilateral, so all angles=60 and all circumferences in front of A ,B and C are same. so if circumference in front of 2 angles = 2pi, so circumference in front of one angle is pi.
so
pi= 60/360*2pi*R
so pi=1/6*2pi*R
so pi=1/3pi*R
R=3....

i hope it is clean what I wrote here.
so what is wrong with it?

In your formula 60 degrees is the measure of the inscribed angle and you should use the measure of the central angle which is twice the inscribed angle so 120 degrees.

Check this: math-circles-87957.html

Arc Length The formula the arc measure is: $$L=2\pi{r}\frac{C}{360}$$, where C is the central angle of the arc in degrees. Recall that $$2\pi{r}$$ is the circumference of the whole circle, so the formula simply reduces this by the ratio of the arc angle to a full angle (360). By transposing the above formula, you solve for the radius, central angle, or arc length if you know any two of them.
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Re: Equilateral triangle is inscribed in a circle. If length of arc ABC is  [#permalink]

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05 Mar 2011, 09:41
oh, now it is clear)thank you very much!!!=)))
Manager
Joined: 29 May 2017
Posts: 125
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: Equilateral triangle is inscribed in a circle. If length of arc ABC is  [#permalink]

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12 Oct 2018, 06:42
Bunuel wrote:
banksy wrote:
164 Equilateral triangle is inscribed in a circle. If length of arc ABC is 2pi, what is the radius of the circle?
(A) 1
(B) 3/2
(C) 2
(D) 5/3
(E) 3

Arc ABC is $$\frac{2}{3}$$ of the circumference (as ABC is equilateral triangle then (arc AB)=(arc BC)=(arc AC), so (arc AB)+(arc BC)=(arc ABC)=2/3 of circumference, so $$arc \ ABC=2\pi$$ basically means that the circumference is $$3\pi$$ --> $$circumference=2\pi{r}=3\pi$$ --> $$r=\frac{3}{2}$$.

Similar question: http://gmatclub.com/forum/geometry-circ ... 97393.html

Bunuel
i think the official answer is wrong. It should be B but it says C.
regards
Re: Equilateral triangle is inscribed in a circle. If length of arc ABC is   [#permalink] 12 Oct 2018, 06:42
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