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?