\(AB\) and \(CD\) are two perpendicular diameters of a uniform circular metal disc of radius \(\quantity{12}{in.}\) and centre \(O\). Two circular holes of radii \(\quantity{4}{in.}\) and \(\quantity{2}{in.}\) are cut out of the disc, their centres being \(\quantity{6}{in.}\) from \(O\) along \(OA\) and \(\quantity{10}{in.}\) from \(O\) along \(OC\) respectively. Find

  1. the distances of the centre of gravity, \(G\), of the remaining portion of the disc from the diameters \(CD\) and \(AB\);
  2. the angle that \(OA\) will make with the vertical if this remaining portion is hung on a smooth pivot at \(O\).