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A circle of radius 1 is randomly placed in a rectangle $ABCD$ so that the circle lies completely inside the rectangle. Length and breadth of rectangles are 36 and 15 respectively.

Let the probability that the circle will not touch diagonal $AC$ be $\dfrac mn$. Here $m$ and $n$ are relatively prime positive integers.

Find the value of $m + n$.

I think this can be done by calculating area. But I am unable to get it how. Also the diagonal length will be 39 .

How can I achieve this?

  • 0
    Out of curiosity, where does this problem come from? Asking for the sum of numerator and denominator of a rational number does sound like a rather strange requirement for a real-world problem.2012-10-23
  • 0
    Found this problem in one PnC book.2012-10-23

2 Answers 2