Question

Longest chord of the circle is
$\begin{align}
  & \text{a) Diameter} \\
 & \text{b) Chord} \\
 & \text{c) Radius} \\
 & \text{d) None} \\
\end{align}$

Answer 1

Hint: Now a chord is nothing but a line segment joining any two points on the circle. The longest chord of the circle will be nothing but the chord passing through the center. The chord passing through the center of the circle is called diameter.

Complete step-by-step answer:
Now we want to find what the longest chord in the circle is.
Now first let us understand some common terms used while drawing figures in geometry.
First consider the 0 dimensional object called point.
A point is nothing but a dot. It has no length and no breadth.
For example take point A.

Now let us understand the concept of line segment. Line segment is nothing but a straight line joining two points. Now we have two points A and B then there can be only one line passing through those two points. And the line segment will be called line segment AB.
For example consider,

Now let us understand the geometrical figure circle. A circle is a figure in which all the points are equidistant from a particular point. That particular point is called the center of the circle and the equal distant between any point on circle and the center is called the radius.
Let us draw a circle with center A.

Now a line segment joining any two points on the circle is known as chord of circle.
For example consider the following line segments.

Now in this figure PQ, ST and LM are chords of the circle with center A.
Now we know that the longest chord of the circle passes through the center.
And the chord that passes through the center is called the diameter. Hence the longest chord is the diameter of the circle.

So, the correct answer is “Option A”.

Note: Now note that diameter is nothing but twice of radius hence if r is the radius of the circle then the longest chord which is the diameter is 2r. Now consider the example in which ST is the diameter we know that SA and AT are radii as they are line segments joining the center and points on the circle. Hence we have AS = AT = r. hence ST = AS + AT = r + r = 2r.