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diameter of circle

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by g.shankaran » Sun Jun 05, 2011 1:40 am
1. An equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

a. 5
b. 8
c. 11
d. 15
e. 19
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by Frankenstein » Sun Jun 05, 2011 1:49 am
Hi,
The arc ABC subtends 240 degrees at the center. So arc length = (4Pi/3)R = 24 =>2R = 24.3/(2Pi)=36/Pi =~ 11.
Hence, C
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by cans » Sun Jun 05, 2011 1:52 am
As ABC is equilateral triangle, arc AB=BC=AC = circumference/3
ABC=24 -> 2AB=24 ->AB=12
Thus circumference=12*3=36
diameter = circumference/pi = 36/3.16 which is nearly equal to 11
IMO C
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by finites » Sun Jun 05, 2011 2:15 am
circumference = 2*pi*r = d * pi --- 1

As ABC is Equilateral triangle, it cuts circle into equal parts.
ab = bc = ac --- 2

ab + bc = 24; --- 3
from 2 and 3.
ab = bc = ac =12.

circumference = ab + bc +ac = 36

from 1
36 = pi *d

d = 36 * 7 /22

d ~ = 11
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by sunilramu » Sun Jun 05, 2011 9:17 am
Given that the arc inscribes 2 of the 3 equal sides of the triangle. The defined arc will form the 2/3rd of circumference the circle.
Therefore,

2/3 * Pi. D = 24
=> D = 36/Pi ~ 11
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by sandeep800 » Sun Jun 05, 2011 10:28 am
IMO C is correct
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by aftableo2006 » Sun Jun 05, 2011 11:22 pm
s=r*angle subtended at the centre by the arc
here 2r*120degree=24
so diameter=24*3/pi=11
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by smackmartine » Sun Jun 05, 2011 11:27 pm
+1 for C
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