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# A point is moving randomly inside an equilateral triangle

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Senior Manager
Joined: 05 Jun 2008
Posts: 294
A point is moving randomly inside an equilateral triangle [#permalink]

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15 Oct 2008, 06:48
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A point is moving randomly inside an equilateral triangle whose side length is 3 cm. What is the probability that its distance to any corner is greater than 1 ???
Senior Manager
Joined: 31 Jul 2008
Posts: 280

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15 Oct 2008, 17:25
form me it some thing like :

1-[44/63*root(3)]

i know its weird
SVP
Joined: 17 Jun 2008
Posts: 1504

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16 Oct 2008, 01:42
9/16 for me.

Total area of triangle = (1/2)*3*(3sqrt3)/2 = 9*sqrt3)/4

Area of three "part of circle with radius 1" = 3*pi*1/6 as the angle is 60 degree.

Hence, the area within which the point can move = 9*sqrt3)/4 - pi/2

And, probability = [9*sqrt3)/4 - pi/2]/[9*sqrt3)/4] which is approx 9/16.
Re: PSP005   [#permalink] 16 Oct 2008, 01:42
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