Question

In the figure O is the centre of the circle OB$=$5 cm , Distance from O to cord AB is 3 cm. Find the length of AB.

Answer 1

Given:$OB=5cm$

$OP=3cm$

$\Rightarrow {PB}^2={OB}^2-{OP}^2$

$\Rightarrow {PB}^2=5^2-3^2=25-9=16$

$\Rightarrow PB=4cm$

Join $OA$

$\Rightarrow OA=OB=$ radius of the circle.

$OP=OP$(common)

$\angle APO=\angle OPB={90}^{\circ }$

$\therefore △APO\cong △OPT$ by SAS congruency criterion

$\Rightarrow AP=PB$ by CPCT

$\therefore AP=PB=4cm$

Hence $AB=AP+PB=4+4=8cm$