Question

Radius of a circle with centre $O$ is $41$ units. Length of a chord $PQ$ is $80$ units, find the distance of the chord from the centre of the circle.

Answer 1

Given, radius $=41units$

Length of chord $PQ=80units$

We know that, perpendicular drawn from the centre of the circle to the chord bisects the chord.
$\therefore PR=RQ=\frac{80}{2}units=40units$
In $△OPR,$
$O{R}^2+P{R}^2=O{P}^2$
$\Rightarrow O{R}^2+{40}^2={41}^2$

$\Rightarrow O{R}^2+1600=1681$
$\Rightarrow O{R}^2=1681-1600$
$\Rightarrow O{R}^2=81$
$\Rightarrow OR=9$

Thus, the distance of the chord from the centre of the circle is $9units$.