In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Solution:

Given that the diameter of the circle = 40 cm and the length of the chord is 20 cm.

⇒ Radius of the circle = half of diameter = 20 cm.

Let AB be the chord whose length is 20 cm ( given)

By joining the radii to the ends of the chord, we get a triangle AOB.

In triangle AOB, OA = OB = 20 cm (radii of the circle)

AB = 20 cm (given the length of the chord)

∴ Triangle AOB is an equilateral triangle with all sides equal.

⇒ Θ = 60° = π / 3 radian.

As we know that, in a circle of radius r unit, if the length of the arc is l unit subtends at an angle Θ radian at the center, then l = r × Θ

⇒ l = 20 × π / 3

⇒ l = 20 π/3 cm.

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.1 Question 5

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Summary:

Given that in a circle of diameter 40 cm, the length of a chord is 20 cm. The length of minor arc of the chord is 20 π/3 cm.