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# Equilateral triangle ABC is inscribed within a circle as shown above.

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Math Expert
Joined: 02 Sep 2009
Posts: 60687
Equilateral triangle ABC is inscribed within a circle as shown above.  [#permalink]

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06 Jun 2017, 09:51
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15% (low)

Question Stats:

77% (01:26) correct 23% (02:10) wrong based on 79 sessions

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Equilateral triangle ABC is inscribed within a circle as shown above. If the circle has an area of 36π, what is the length of minor arc AC?

A. 3π

B. 4π

C. 5π

D. 6π

E. 9π

Attachment:

EquilateralCircle.png [ 8.51 KiB | Viewed 1362 times ]

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Equilateral triangle ABC is inscribed within a circle as shown above.  [#permalink]

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06 Jun 2017, 10:11
Bunuel wrote:

Equilateral triangle ABC is inscribed within a circle as shown above. If the circle has an area of 36π, what is the length of minor arc AC?

A. 3π

B. 4π

C. 5π

D. 6π

E. 9π

Attachment:
EquilateralCircle.png

Triangle ABC is equilateral, thus minor arcs AC, AB, and BC are equal and each is 1/3rd of the circumference (since these 3 arcs make the whole circumference).

were given that the area of the Circle is 36π, using the area formula we can derive the radius and then the circumference.

$$π*r^2$$ = 36π, then the radius r is 6

using the circumference formula of a Circle
$$2*π*r = 2*π*6 = 12π$$

then minor arc AC: $$\frac{12π}{3} = 4π$$

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Re: Equilateral triangle ABC is inscribed within a circle as shown above.  [#permalink]

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08 Dec 2019, 20:29
Bunuel wrote:

Equilateral triangle ABC is inscribed within a circle as shown above. If the circle has an area of 36π, what is the length of minor arc AC?

A. 3π

B. 4π

C. 5π

D. 6π

E. 9π

Attachment:
EquilateralCircle.png

Minor arc AC is 1/3 of the circumference.

Since the area of the circle is 36π, the radius is 6, and thus, the circumference is 12π. Minor arc AC is therefore 1/3 x 12π = 4π.

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Joined: 16 Dec 2019
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Re: Equilateral triangle ABC is inscribed within a circle as shown above.  [#permalink]

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29 Dec 2019, 02:11
Minor arc AC is 1/3 of the circumference
Can somebody explain this ?
Re: Equilateral triangle ABC is inscribed within a circle as shown above.   [#permalink] 29 Dec 2019, 02:11
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