Find the length of the tangents drawn from an external points as shown in below fig. and distance between the centre of the circle to the external point is 13cm and length of diameter is 10cm

Given diameter $\left(d\right)=10\text{cm}$

$r=5\text{cm}$

In $\Delta OAP,\angle A=90°$

From Pythagoras theorem $O{P}^2=O{A}^2+A{P}^2$

${\left(13\right)}^2={\left(5\right)}^2+A{P}^2$

$P{A}^2={\left(13\right)}^2-{\left(5\right)}^2$

$PA=\sqrt{169-25}=\sqrt{144}=12$

$PA=12\text{cm}$

$\therefore PB=12\text{cm}$    ($\because$ From external point. Tangents lengths are equal)

$\therefore PA=PB=12\text{cm}$