Question

A chord of a circle, which is twice as long as its radius is diameter of the circle.
A. True
B. False

Answer 1

Hint: To check whether the given statement is true or false, we will construct a circle. Now, we will draw a straight line from the centre of the circle to the circle’s circumference. We know that this line is called the radius of the circle. Now, we will extend this line to the other end such that the end of the straight line lies on the circle’s circumference. The diameter of the circle is the line that passes through the centre of the circle and whose endpoint lies on the circle. We will conclude from the construction whether the given statement is true or false.

Complete step-by-step answer:
The following is the schematic diagram of the circle.

We can define the chord as a line segment drawn by joining any two points on the circle's circumference. In other words, the chord is a straight line whose endpoints lie on the circle.
To check the given statement, we will first define the radius of the circle. In the first figure, a straight line is drawn from the centre of the circle to the circle's circumference. This straight line is called the radius of the circle. When we extend this line to the other end, the length of the straight line will be twice the radius. But, we know that segment passing through the centre of the circle and whose endpoint lies on the circle is the circle's diameter. Hence, we can say that the diameter is twice the radius and the given statement is true.
So, the correct answer is “Option A”.

Note: There is another term related to a circle, which is the tangent of a circle. We can get confused between the terms chord and tangent of the circle. The difference between chord and tangent of the circle is that chord is described as the straight line drawn by joining any two points on the circle’s circumference, but the tangent of a circle is a line that touches only a single point at the circle.