In the adjoining figure, O is the centre of the centre of the circle. If diameter AC=26cm and chord AB=10cm, then find the distances of the chord AB from the centre of the circle.

Explanation

Radius of circle `=("diameter")/(2)`
`rArr AO=(26)/(2)=13cm`
`AM=(AB)/(2)=(10)/(2)=5cm, (because "perpendicular drawn from centre to the chrod bisects the chord" )`
Now, in `Delta AOM`,
`AM^2+OM^2=AO^2`
`rArrOM^2=AO^2-AM^2=13^2-5^2=169-25=144`
`rArrOM=sqrt(144)=12 cm`
Therefore, the distance of chord from the centre =12 cm