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# A point is randomly chosen inside the unit square ABCD such that angle

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VP
Joined: 19 Oct 2018
Posts: 1294
Location: India
A point is randomly chosen inside the unit square ABCD such that angle  [#permalink]

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06 Dec 2019, 20:04
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00:00

Difficulty:

95% (hard)

Question Stats:

15% (02:09) correct 85% (02:08) wrong based on 38 sessions

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A point is randomly chosen inside the unit square ABCD such that angle APB is equal to x. What is the probability that angle x is obtuse ?

A. 0.1

B. 0.2

C. 0.3

D. 0.4

E. 0.5

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Math Expert
Joined: 02 Aug 2009
Posts: 8337
A point is randomly chosen inside the unit square ABCD such that angle  [#permalink]

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07 Dec 2019, 06:41
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1
nick1816 wrote:
A point is randomly chosen inside the unit square ABCD such that angle APB is equal to x. What is the probability that angle x is obtuse ?

A. 0.1

B. 0.2

C. 0.3

D. 0.4

E. 0.5

Now when will x be 90— when AB is a diameter and a semi circle is drawn with AB as diameter.
So, P can be anywhere on the semicircle.
Any point within this semi circle will give an angle >90.

Probability =area of semicircle/area of square
Area of semicircle =$$\frac{1}{2}*\pi*(\frac{AB}{2})^2=\frac{\pi*AB^2}{8}$$
Area of square = $$AB^2$$..

Probability =$$\frac{\pi*AB^2}{8AB^2}=\frac{\pi}{8}=\frac{22}{56}$$=~0.4

D
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A point is randomly chosen inside the unit square ABCD such that angle   [#permalink] 07 Dec 2019, 06:41
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