Question

In a circle of radius 7 cm, tangent PT is drawn from a point P, such that PT = 24 cm. If O is the centre of the circle, then OP = ?


(a) 30 cm
(b) 28 cm
(c) 25 cm
(d) 18 cm

Answer 1

(c) 25 cm
The tangent at any point of a circle is perpendicular to the radius at the point of contact.
$$\begin{gathered} \therefore OT\perp PT \\ \mathrm{From}\mathrm{}\mathrm{right}-\mathrm{angled}\mathrm{}\mathrm{triangle}PTO, \\ \therefore O{P}^2=O{T}^2+P{T}^2[\mathrm{U}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{}\mathrm{P}\mathrm{y}\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{g}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{s}\text{'}\mathrm{}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{m}] \\ \Rightarrow O{P}^2={\left(7\right)}^2+{\left(24\right)}^2 \\ \Rightarrow O{P}^2=49+576 \\ \Rightarrow O{P}^2=625 \\ \Rightarrow OP=\sqrt{625} \\ \Rightarrow OP=25\mathrm{cm} \end{gathered}$$