Question

In the figure, radius of the circle with centre at $O$ is $6$ centimetres. And $PA=4cm,PB=5cm$. Find the length of $OP$.

Answer 1

From $O$, draw $OD\perp AB$
$AB=AP+PB=4+5=9cm$
$\Rightarrow$ $AD=4.5cm$
In right $△OAD$,
$OD=\sqrt{{OA}^2-{AD}^2}=\sqrt{6^2-{4.5}^2}=\sqrt{36-20.25}=\sqrt{15.75}$
$PD=AD-AP=4.5-4=0.5cm$
In right $△OPD$,
$OP=\sqrt{{OD}^2+{PD}^2}=\sqrt{15.75+{0.5}^2}=\sqrt{15.75+0.25}=\sqrt{16}=4cm$