diameter of circle

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g.shankaran: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue Oct 27, 2009 8:19 am; Thanked: 4 times; Followed by:2 members

diameter of circle

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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Source: Beat The GMAT — Problem Solving | Sun Jun 05, 2011 1:40 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 am; Location: India; Thanked: 375 times; Followed by:53 members

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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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

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
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finites: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jun 02, 2011 7:21 am

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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sunilramu: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu Feb 24, 2011 4:47 am; Thanked: 1 times

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