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Given a rectangle containing uniformly distributed random points, how far are the points from the rectangle's centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided. 2010 Mathematics subject classification: primary 60D05; secondary 68T40.doi:10.1017/s0004972712000421 fatcat:2teikvzpvne63muvdxsuqenu7a