Question

What is the maximum number of regions that three chords of a circle could divide the circle into?

Answer 1

Answer:

6

Step-by-step explanation:

6 is the maximum number of regions that three chords of a circle could divide the circle into?

Answer 2

The maximum number of regions that three chords of a circle could divide the circle into is equal to 7.

Step-by-step explanation:

→ The chord of a circle is a line segment that joins any two points lying on the circumference of the circle. If the chord passes through the centre of the circle then it is known as the diameter.

→ A chord divides the circle into two regions. The bigger region is known as the major segment whereas the smaller region is known as the minor segment.

→ If the number of chords of the circle is equal to 'n', then the formula for maximum number of regions that the circle gets divided into is given as:          

                    $Maximum\:number\:of\:regions=\frac{n(n+1)}{2}+1$

→ In the case of 3 chords 'n' is equal to 3, therefore the maximum number of regions would be equal to:

                   $\therefore Maximum\:number\:of\:regions=\frac{n(n+1)}{2}+1\\\\\therefore Maximum\:number\:of\:regions=\frac{3(3+1)}{2}+1\\\\\therefore Maximum\:number\:of\:regions=6+1=7$

Therefore the maximum number of regions that three chords of a circle could divide the circle into is equal to 7.

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