Question

Radius of circle is $10cm$. There are two chords of length $16cm$ each. What will be the distance of these chords form the centre of the circle?

Answer 1

Length of the chord AB$=16$cm and radius$\left(r\right)=10$cm.

To find:- OM

Construction: Draw a perpendicular OM from centre O such that it bisects the chord AB

Proof: In right angled $\Delta OMB$

$O{B}^2=O{M}^2+B{M}^2$

$\Rightarrow (10{)}^2=O{M}^2+(8{)}^2$

$\Rightarrow 100=O{M}^2+64$

$\Rightarrow O{M}^2=100-64$

$\Rightarrow O{M}^2=36$

$\Rightarrow OM=\sqrt{36}$

$\Rightarrow OM=6$cm

$\therefore$ Hence, the distance of the chord from the centre of the circle is $6$cm.