Find the length of the chord which substends an angle of `110^(@)` at the centre of the circle of radius 7 cm.

Explanation

Let the chord be AB. O be the centre of the circle and OD is shortest distance of the chord from the centre of circle.
Given `OA=OB=7cm, angleAOB=110^(@)`.
clearly, `DeltaAOD congDeltaBOD` by SSS axiom
`angle AOD=angleBOD=(1)/(2)angleAOB=55^(@)`.
In`DeltaAOD`,
`sin55^(@)=(AD)/(AO)`
`0.8192= (AD)/(7)`
AD=5.7344.
The length of the chord = 2AD
`=2(5.7344)`
`=11.4688 cm`.