Imagine placing a line segment P of length a on the XY plane such that its middle is at the origin, but its orientation is random (i.e. random angle). Then suppose you placed another line segment Q of length b (which is less than or equal to a) such that its centre was randomly chosen within a radius (a+b)/2 from the origin, but its orientation was also random. What would the probability of these two line segments intersecting be?
I suspect there may be an integral over the circular surface to be done here, but am not quite sure what to do! Any help much appreciated. Thank you.
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