The centre of a circular disc of radius \(r\) is \(O\), and \(P\) is a point on the line through \(O\) perpendicular to the plane of the disc such that \(OP=p\). Prove that the mean distance with respect to area of points of the disc from \(P\) is \[ \frac{2}{3r^2}\{(p^2+r^2)^{3/2}-p^3\}. \] Find the mean distance with respect to volume of the interior points of a sphere of radius \(a\) from a fixed external point at distance \(c\) from its centre.