Question

A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is

Answer 1

In a circle, chord AB = 14 cm

and distance from centre, OL = 6 cm

Let r be the radius of the circle, then $O{A}^2=A{L}^2+O{L}^2$

$\Rightarrow r^2=(7{)}^2+(6{)}^2=49+36=85$

In the same circle length of another chord CD = ?

Distance from centre = 2 cm

$\therefore r^2=O{M}^2+M{D}^2$

$\Rightarrow 85=(2{)}^2+D{M}^2$

$\Rightarrow 85=4+D{M}^2$

$\Rightarrow D{M}^2=85-4=81=(9{)}^2$

$\therefore DM=9$

$\therefore CD=2\times DM=2\times 9=18cm$

$\therefore$ Length of another chord = 18 cm