The length of the tangent drawn from a point $P$, whose distance from the centre of a circle is 25 c

Question

The length of the tangent drawn from a point $P$, whose distance from the centre of a circle is 25 cm , and the radius of the circle is 7 cm , is :\

Professor PC Thomas Classes · Answer

(b): Let $P A$ be the tangent to the circle and $O$ be the centre of the circle.\ $	herefore \quad O P=25 \mathrm{~cm}$ and $O A=7 \mathrm{~cm}$\ Since, $P A \perp O A$ ( ∵ Tangent is perpendicular to the radius at the point of contact)\ $	herefore \quad$ By Pythagoras theorem, $O P^{2}=P A^{2}+O A^{2}$\ $\Rightarrow \quad P A^{2}=O P^{2}-O A^{2}=(25)^{2}-(7)^{2}=625-49=576$\ $\Rightarrow P A=24 \mathrm{~cm}$\ $	herefore \quad$ The length of the tangent is 24 cm .\