Question

Is every chord of a circle also a diameter?

Answer 1

Hint – In this particular question use the concept that the chord of the circle is a line joining two points on the circle i.e. points on the circumference of the circle whereas diameter of the circle is always passing through the center of the circle so use these concepts to reach the solution of the question.

Complete step by step solution:

Let us consider a circle having a center on O as shown above in the diagram.
Now let us consider points A, B, C, and D on the circumference of the circle as shown in the above figure.
Now as we know that the chord of the circle is a line joining two points on the circle.
And the diameter of the circle is always passing through the center of the circle.
So join point A and D, C and D and C, O and B as shown in the above figure.
So according to the definition of the chord all of the lines i.e. AD, CD and CB are the chords of the circle, but according to the definition of the diameter of the circle only CB is the diameter as this is the only line which is passing through the center of the circle.
So we can say that every chord of the circle does not represent the diameter of the circle.
So this is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember is that the diameter of the circle is the longest chord of the circle, it is a chord but every chord of the circle does not represent the diameter of the circle as shown in the above figure.