The discus throw is an event in which an athelete attempts to throw a discus. The athlete spins anti-clockwise around one and a half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.
In the given figure, \(AB\) is one such tangent to a circle of radius \(63 \ cm\). Point \(O\) is centre of the circle and \(\angle ABO = 30^\circ\). \(PQ\) is parallel to \(OA\).
Based on the above information:
(a) The length of \(AB\) is __________\(cm\)
(b) The length of \(OB\) is ___________ \(cm\)
(c) The length of \(AP\) is __________ \(cm\)
(d) The length of \(PQ\) is __________ \(cm\)