Question

The radius of the circle is $10\text{cm}$ and the length of one of its chords is $12\text{cm}$, then the distance of the chord from the center is

Answer 1

In $△AOB,$

$AB=6\text{cm}$ (Half of chord $AC$)

Radius of circle $AO=10\text{cm}.$

By Pythagoras theorem,

$\begin{array}{cc}A{O}^2& =A{B}^2+O{B}^2\\ {10}^2& =6^2+O{B}^2\\ 100-36& =O{B}^2\\ O{B}^2& =64\\ OB& =8\text{cm}\end{array}$

Hence, the distance of the chord from the center is equal to $8\text{cm}.$