Question

In the given figure, $AB$ is a chord of length $9.6cm$ of a circle with centre $O$ and radius $6cm$.The tangent at $A$ and $B$ intersect at $P$. Find the length of $PA$.

Answer 1

Now $\Delta AMP\sim \Delta AOP$

(AA critical)

$\angle PAO=\angle PMP\left({90}^o\right)$

$\angle P=\angle P$(Common)

So, $\frac{PA}{OP}=\frac{AM}{OA}$

$\frac{PA}{OP}=\frac{4.8}{60}$

$\frac{PA}{OP}=\frac{4}{5}$

$AB=9.6$As $\Delta AOP$ and $\Delta BPO$

$AP=BP$ (tangent)

$AO=OB$ (redians)

$OP=OP$ (common)

$\Delta AOP\cong \Delta BPO$

So, $AM=MB$

So, $\frac{9.6}{2}=4.8$