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A point is moving randomly inside an equilateral triangle

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Senior Manager
Senior Manager
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Joined: 05 Jun 2008
Posts: 304

Kudos [?]: 182 [0], given: 0

A point is moving randomly inside an equilateral triangle [#permalink]

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New post 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 ???

Kudos [?]: 182 [0], given: 0

Senior Manager
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Joined: 31 Jul 2008
Posts: 290

Kudos [?]: 55 [0], given: 0

Re: PSP005 [#permalink]

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

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

i know its weird :shock:

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SVP
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Joined: 17 Jun 2008
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Re: PSP005 [#permalink]

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New post 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.

Kudos [?]: 279 [0], given: 0

Re: PSP005   [#permalink] 16 Oct 2008, 01:42
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A point is moving randomly inside an equilateral triangle

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