A circular region has a radius of \(13 m\). Students place two rows of flags along equal chords \(XY\) and \(MN\) with the measurement of \(24 m\), each at the same distance from the centre.
(i) Determine the perpendicular distance from the centre \(O\) to each chord.
(ii) If another group places a chord \(PQ\) at a distance of \(12 m\) from the centre. Determine its length.
(iii) Two equal chords in a circle are at distances of \(4 cm\) and \(9 cm\) from the centre. Is this construction possible?
(iv) State the general relation between chord length and distance from the centre.