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# In the figure above, inscribed ∆ ABC is equilateral.If the radius of

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Joined: 02 Sep 2009
Posts: 50007
In the figure above, inscribed ∆ ABC is equilateral.If the radius of  [#permalink]

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14 Nov 2017, 01:05
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:03) correct 24% (01:58) wrong based on 45 sessions

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In the figure above, inscribed ∆ ABC is equilateral.If the radius of the circle is r, then the length of arc AXB is

(A) 2πr/3
(B) 4πr/3
(C) 3πr/2
(D) πr^2/3
(E) 2πr^2/3

Attachment:

2017-11-14_1155_001.png [ 6.85 KiB | Viewed 599 times ]

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Re: In the figure above, inscribed ∆ ABC is equilateral.If the radius of  [#permalink]

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14 Nov 2017, 02:33
Bunuel wrote:

In the figure above, inscribed ∆ ABC is equilateral.If the radius of the circle is r, then the length of arc AXB is

(A) 2πr/3
(B) 4πr/3
(C) 3πr/2
(D) πr^2/3
(E) 2πr^2/3

Attachment:
2017-11-14_1155_001.png

Since the Triangle is an Equilateral triangle so it will divide teh circumference in 3 equal parts

i.e. Arc AXB = (1/3)*Circumference of Circle

i.e. Arc AXB = (1/3) 2πr

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Re: In the figure above, inscribed ∆ ABC is equilateral.If the radius of  [#permalink]

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14 Nov 2017, 02:55
4
Its a simple concept: Angle created by a chord at center is double the angle created on the circumference.

As angle ACB is 60 degress, so angle created by the chord AB at the center would be 120 degrees.

Total circumference of the circle for 360 degrees is: 2nr

so length of 120 degrees will be 2nr/3. Hence option A
Re: In the figure above, inscribed ∆ ABC is equilateral.If the radius of &nbs [#permalink] 14 Nov 2017, 02:55
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