What is the maximum number of regions into which a chord will divide a circle? (a) 1 (b) 2 (c) 3 (d) 4
Hint: Here first we will understand the term of the circle known as the ‘chord’. Now, we will use a diagram of a circle with a chord to observe the situation geometrically. Further we will know the names of the segments which are formed due to the chord of the circle.
Complete step by step solution: Here we have been asked to find the maximum number of regions into which a circle is divided by a chord. First we need to understand the meaning of the term ‘chord’ of a circle. Now, a chord of a circle is a line segment (straight) that joins any two pints on a circle. It may pass through the origin of the circle. Let us draw a figure to better understanding.
In the above figure we have two points A and B lying on the circle. When we join these two points to form a line segment AB then that line segment AB is called the chord of the circle. Clearly we can see that the circle is divided into two parts or segments. The segment whose area is greater is known as the major segment while the other segment is known as the minor segment. Therefore, a chord of a circle divided it into two parts only. Hence, option (b) is the correct answer.
Note: Note that if the chord of a circle passes through its center then it is called the diameter of the circle, so we can say that the diameter is the longest chord of a circle. Half of the diameter is called the radius of the circle but half of a chord is never called the radius of the circle unless that chord is specified as the diameter.