Study the uniqueness of a circle determined by a given centre and radius.
a. (a) State the postulate that allows a circle to be constructed when a centre and a radius are given.
b. (b) Given a fixed point O and a fixed length 5cm, prove that not more than one circle can be drawn having centre O and radius 5cm.
c. (c) If another circle is drawn with centre O and radius 5cm, what can you conclude about the set of points common to the two circles? Justify your answer.