Study the uniqueness of a circle determined by a given centre and radius.
MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Euclid's Geometry · Introduction to Euclid's Geometry
Problem
Study the uniqueness of a circle determined by a given centre and radius.
(a) State the postulate that allows a circle to be constructed when a centre and a radius are given.
(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) 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.