Question

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

Answer 1

As perpendicular from origin also bisects the chord

$\Rightarrow BP=40$ units.

By Pythagoras theorem in $\Delta OPB$,

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

$\Rightarrow O{P}^2={41}^2-4{)}^2$

$\Rightarrow O{P}^2=81\times 1$

$\Rightarrow OP=\sqrt{81}$

$\Rightarrow OP=9cm$.