A circle may be described with any centre and any ____.

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Detailed Solution

A circle may be described with any centre and any radius.
Given a circle.
Euclid assumed certain properties, that are not to be proved. These assumptions are actually ‘obvious universal truths’.
He divided these into two types: axioms and postulates.
He used the term ‘postulate’ for the assumptions that were specific to geometry.
Common notions (often called axioms), on the other hand, were assumptions used throughout mathematics and not specifically linked to geometry.
Euclid’s postulates are:
Postulate 1: A straight line may be drawn from any one point to any other point.
Postulate 2: A terminated line can be produced indefinitely.
Postulate 3: A circle can be drawn with any centre and any radius.
Postulate 4: All right angles are equal to one another.
Postulate 5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
Thus, a circle may be described with any center and any radius.
Therefore, the correct answer is radius.

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