Question

in a circle of diameter 40cm,the length of a chord is 20cm. find the length of minor arc of the chord

Answer 1

Step-by-step explanation:

Diameter of the circle =40 cm

∴ Radius (r) of the circle =

2

40

=20 cm

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

In △OAB, OA = OB = Radius of circle = 20 cm

Also, AB = 20 cm

Thus, △OAB is an equilateral triangle.

∴θ=60

∘

=

3

π

radian

We know that in a circle of radius r unit, if an arc of length I unit subtends an angle θ radian at the centre, then θ=

r

l

∴

3

π

=

20

arc AB

⟹arc AB=

3

20

π cm