Question

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is _______.

Answer 1

PT is a tangents drawn from P to circle with centre O.

PT = 10 cm and OT = 5 cm (Radius of the circle)

Now,

∠OTP = 90º (Radius is perpendicular to the tangent at the point of contact)

In right ∆OTP,

$$\begin{gathered} {\mathrm{OP}}^2={\mathrm{OT}}^2+{\mathrm{PT}}^2\left(\mathrm{Pythagoras}\mathrm{theorem}\right) \\ \Rightarrow {\mathrm{OP}}^2={\left(5\right)}^2+{\left(10\right)}^2 \\ \Rightarrow {\mathrm{OP}}^2=25+100=125 \\ \Rightarrow \mathrm{OP}=5\sqrt{5}\mathrm{cm} \end{gathered}$$

Thus, the distance of the point from the centre of the circle is $5\sqrt{5}$ cm.


The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is $\underline{5\sqrt{5}\mathrm{cm}}$.