Question

In a circle of diameter 40 cm the length of a cord is 20 cm. Find the length of minor arc corresponding to the cord.

Answer 1

Using the property that perpendicular from the centre bisects the chord, we can say that PC= 10cm. (half of chord AC)

=>$\angle POC=si{n}^{(}-1\left)\right(\frac{10}{20})=30$

=>$\angle AOC=60$

Lenght of arc $OABC=r\theta ,where\theta =\angle AOC$

=> lenght= $20\times \frac{\pi }{3}=20.9cm$