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Math Help - rectangle

  1. #1
    Senior Member Sampras's Avatar
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    rectangle

    Consider the unit circle C:  x^2+y^2 = 1 . Suppose 2 points are chosen randomly: (i)  p is chosen from the circumference and (ii)  q is chosen from the interior (chosen independently). Let  R be the rectangle with diagonal  pq . What is the probability that no point of R lies outside of C?

    Wouldn't a rectangle with diagonal  pq always lie inside the circle?
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  2. #2
    MHF Contributor
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    The Diagonal pq will always be in or on the circle. Not so the other diagonal.

    Easy demonstration:

    p = <0, 1>

    q = <1-\epsilon , 0>

    Where 0 < \epsilon << 1

    p is the North West Vertex
    q is the South East Vertex

    Where is the North East vertex?
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