Question

Fill in the blanks:

A circle divides the plane, on which it lies, into ______ parts.

And explain how?

Answer 1

3 parts

Yes! When a circle is drawn on a plane of sheet,

We get 3 different sets of points. Because circle has no end points like a segment has. Or a circle can not be extended up to infinity , where as a line can be. So, a line divides the plane only in 2 parts( 2 different SETS of points) exterior & interior, that is on the line.

Circle divides tha plane into 3 parts. One is the SET of points in the interior region of the circle.

Second one is the SET of points in exterior region of the circle.

And the third one is the SET of points on the Circle..

And these three different sets hold different properties , when related to the properties of circle….