A chord 10cm long is drawn in a circle whose radius is `5sqrt(2)` cm. Find the area of both the segments.

Answer

`14.25cm^(2),2744.7cm^(2)`

Explanation

Let `OA=5sqrt(2)cm, OB=5sqrt(2)cm` and `AB=10cm`
Then `OA^(2)+OB^(2)=AB^(2)implies/_AOB=90^(@)`
ar (minor segment ACBA)
`=` ar (sector OACBO) `-ar(DeltaOAB)`
`={(3.14xx(5sqrt(2))^(2)xx90)/360-1/2xx5sqrt(2)xx5sqrt(2)}cm^(2)`

`=57/4cm^(2)=14.25cm^(2)`
ar (major segment) `={3.14xx(5sqrt(2))^(2)-14.25}cm^(2)=(157-14.25)cm^(2)`
`=142.75cm^(2)`