Question

How many chords can be drawn through 5 points on a circle ?

• A. 5
• B. 10
• C. 20
• D. 60

Answer 1

The Correct Option is B

To determine the number of chords that can be drawn through 5 points on a circle, we consider the fact that a chord is formed by joining two distinct points. Given 5 points, the number of ways to choose 2 points can be calculated using combinations. This is represented mathematically as C(n, k), where n is the total number of points, and k is the number of points to be selected.

For this problem, n = 5 and k = 2.

The combination formula is given by:

C(n, k) = n! / (k! * (n-k)!)

Substituting the values, we have:

C(5, 2) = 5! / (2! * (5-2)!)

Calculating the factorials, we get:

5! = 5 × 4 × 3 × 2 × 1 = 120

2! = 2 × 1 = 2

3! = 3 × 2 × 1 = 6

Thus, the expression simplifies to:

C(5, 2) = 120 / (2 × 6) = 120 / 12 = 10

Therefore, the number of chords that can be drawn through 5 points on a circle is 10.