Question

State true or false.
The longest of all chords of a circle is called a diameter.
 a) True
b) False

Answer 1

Hint: Here we will find the longest chord of the circle i.e, the line segment whose length is maximum when joined from one point on the circumference of the circle to the other on the circumference.

Complete step-by-step answer:
We know that a chord is a line segment which joins two points on the circumference of a circle.
Also, the longest chord of the circle passes through its center.
Now since the diameter of the circle passes through its center
Hence diameter is the longest chord of the circle.
AB is the diameter of the circle with center as O shown in the figure.
               

Therefore the given statement “The longest of all chords of a circle is called a diameter.” is true.

So, the correct answer is “Option A”.

Additional Information: Circle is the locus of all points which are at equal distance from a fixed point called the center of the circle. The distance between the center and each of the points is called radius of the circle.

Also, on joining all the adjacent points together we get the circumference of the circle.
Now the distance between any two points on the opposite side of the circumference is called the chord of the circle and the chord passing through the center is called its diameter.
Hence diameter is equal to twice the distance between center and the point on circumference.
Therefore, diameter is twice the radius of the radius.
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Note: Students should note that the diameter D of the circle is equal to twice its radius R.
\[D = 2R\]
Also, the diameter divides the circle into two halves.