A chord of length 14cm is at a distance of 6 cm from the center of the circle. The length of another chord at a distance of 2cm from the center of the circle is (a) 12cm (b)14cm (c)16cm (d)18cm

Explanation

In a circle, chord `AB = 14 cm`
distance from centre, `OL = 6 cm`

Let r be the radius of the circle, then,`OA^2=AL^2+OL^2`
`r^2=(7)^2+(6)^2=49+36=85`
In the same circle length of another chord `CD = ?`
Distance from centre `= 2 cm`
`r^2=OM^2+MD^2`
`85=
(2)^2+DM^2`
`85=4+DM^2`
`DM^2=85−4=81=(9)^2`
`DM=9`
`CD=2xxDM=2xx9=18cm`
Length of another chord=`18cm`