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Source: — Problem Solving |
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by clock60 » Sat May 15, 2010 11:02 am
dkumar.83 wrote:Image
i got 12, hope that this ans is close and my reasoning is balid

(240/360)*2*pi*R=24
R=6, D=12
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by dkumar.83 » Sat May 15, 2010 11:05 am
The correct answer is 11. BTW how did u assumed 240degrees?
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by orel » Sat May 15, 2010 11:11 am
We need to find the approximate diameter, which is 2R.

Length of the arc ABC=2/3 of the length of circumference.

The length of circumference is measured as 2ПR

24=2/3*2ПR

2ПR=72/2=36

2R=36/3.14=~11
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by dkumar.83 » Sat May 15, 2010 11:15 am
Hey orel,

How did u assumed that length of d arc is 2/3rd of circumference?
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by clock60 » Sat May 15, 2010 11:22 am
dkumar.83 wrote:The correct answer is 11. BTW how did u assumed 240degrees?
as all angles of triangle are equal the circle is divided on 3 equal arc ab, bc, ca, and each is equal 360/3=120 degrees
so ab+bc=120+120=240

the other way to see that angle abc=1/2* center angle. 60=1/2*center angle. and center angle=120. say aoc=120. then
360-120=240. (i mean external center angle=240)

also i assumed that pi=3 and final answer does`t match exactly
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by orel » Sat May 15, 2010 11:54 am
dkumar.83 wrote:Hey orel,

How did u assumed that length of d arc is 2/3rd of circumference?

It is an equilateral triangle inscribed into a circle, so it divides the circumference of the circle into 3 equal parts. Arc ABC is 2/3 of the circumference.
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