Question

A circle has only a finite number of chords. True or false.

Answer 1

Hint: We should know the definition of chord. It is a line that touches any two points on the circle. Try to draw diagram for better visualisation.

Complete step-by-step answer:
Given statement is: A circle has only a finite number of chords.
Now first get a clear idea of the chord . In a circle what is the concept of chord.
Definition:
A chord is a line drawn from any one point of the circle to any other point on the same circle.
Diagram:

Now if we observe the figure above O is the center of the circle and AB is the chord of the circle.
But we can draw n number of such chords. See in figure drawn below.

Now apart from the brown line we are able to see green lines also. These lines are also drawn from one point of the circle and are touching the other point of the same circle.
Thus we conclude that a circle has an infinite number of chords.
Hence the given statement is false.

Additional information:

The purple line drawn from X to Y passing through the center is called the largest chord of the circle that is diameter.

Note: Don’t get confused with the words of the statement .Only finite is nothing but finite itself. The circle has infinite chords.