Prove that no line is entirely contained in any circle Prove

Solution

Hi,

I hope the following explanation helps you in clear understanding.

From the definition of a circle ,it is a curve ,joining all points which are at equal distances (I.E radius) from a fixed point (I.E centre)

And by joining any two points on the circle ,we get a line segment (chord),which has a limited length.

But for a line ,its length is un limited .

So a line cannot be a line segment, which exist in a circle.so a line cannot be existed in a circle.

Hence proved.

In other words, simply the biggest chord of a circle is its diameter, which has finite length.but a line will have infinite length.

So ,entirely a line cannot be in a circle.