Question

in a circle of diameter 40 cm the length of Chord is 20 cm find the length of minor arc of the chord ​

Answer 1

Answer:

20π3

Step-by-step explanation:

Given:

In a circle of diameter 40 cm the length of Chord is 20 cm find the length of minor arc of the chord ​= ?

Solution:

Diameter=40cm

Length of the chord=20cm

Radius=20cm

Since radius=length of chord=20cm

Hence the formed Δle in the circle is equilateral Δle

⇒θ=60∘

We know that l=rθ

l=20×60∘×π180∘

l=20π3

Thus,

Length of the minor arc of the chord is 20π3

Answer 2

Question

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

Solution

Diameter of the circle = 40 cm

Radius (r) of the circle = 40/2 cm = 20 cm

Let AB be a chord length = 20 cm of the circle.

In ∆OAB,OA = OB = Radius of the circle = 20 cm

Also,AB = 20 cm

Thus,∆OAB is an equilateral triangle.

$\sf{θ = 60 \degree = \dfrac{\pi}{3} radian}$

We know that in a circle of radius r unit,If an arc of length / Unit subtends an angle θ.

$\sf{θ = \dfrac{1}{r}}$

$\sf{\dfrac{π}{3}}$ $\sf{= \dfrac{AB}{20}} →AB$ = 20π/3 cm

Thus the length of the minor arc of chord is $\sf{\dfrac{20π}{3}}cm$