Question

Given three collinear points , then the number of circles which can be drawn through three points is :
a) zero
b) one
c) two
d) infinite

Answer 1

Hint: When points lie on the same straight line , they are called collinear points. Draw three collinear points and try to form a circle.

Complete step-by-step answer:

Given , there are three collinear points . Now , by definition , we know that collinear points are the points which lie on the same straight single line . The question asks how many circles can be drawn through those three collinear points .
Conceptually draw a figure , and it’s a straight line , which passes through the three points . In the figure A B C are three collinear points lying on the same straight line . Thus , no circle can be drawn through those collinear points . The only figure that can be drawn through them is a straight line , on which the three points lie . Hence , we cannot draw a single circle through three collinear points.
Thus the required option for the above question is a) zero

Note: The three collinear points lie on the same straight line , thus making it not possible to draw a circle through them . To draw a circle through the three points , the points need to be non collinear and not lie on the same straight line . Students go wrong in mostly understanding the concept of collinear points and hence end up choosing the wrong option .