Question

What is the distance of the chord of length $16cm$ from the centre of circle, if its radius is $10cm$?

Answer 1

Given,

length of chord $\left(AB\right)=16cm$

radius of circle $\left(r\right)=10cm$

Draw a perpendicular OM from center O to the chord AB, So it bisect the chord.

therefore,

$BM=\frac{AB}{2}=\frac{16}{2}=8cm$

Now, In right $\Delta$OMB

$\begin{array}{c}\Rightarrow O{B}^2=O{M}^2+B{M}^2\\ \Rightarrow {10}^2=O{M}^2+8^2\\ \Rightarrow 100=O{M}^2+64\\ \Rightarrow O{M}^2=36\\ \Rightarrow OM=\sqrt{36}=6cm\\ \Rightarrow OM=6cm\end{array}$

hence,

distance of the chord from center of the circle is $6cm$