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

1 Answer
Dec 13, 2017

I got 20.9cm

Explanation:

Let us have a look at the diagram:
enter image source here
and consider the orange right triangle where the hypotenuse is equal to the radius r=d/2=40/2=20cm and one of the sides is half the length of the chord, 20/2=10cm.
We can evaluate the angle alpha using trigonometry:

10=20sin(alpha)

alpha=arcsin(10/20)=30^@

so that the entire angle theta will be:

enter image source here

theta=2alpha=60^@
in radians this angle is: pi/3.

We can use this value in radians into:

s=rtheta

to find the length of the arc s:

s=20pi/3=20.9cm