Question

Find the length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre of the circle.

Answer 1

$$\begin{gathered} \mathrm{Since},\mathrm{}\mathrm{triangle}\mathrm{}OPT\mathrm{is}\mathrm{}\mathrm{a}\mathrm{}\mathrm{right}-\mathrm{angled}\mathrm{}\mathrm{triangle},\mathrm{}\mathrm{by}\mathrm{}\text{P}\mathrm{ythagoras}\text{'}\text{T}\mathrm{heorem}: \\ O{P}^2=O{T}^2+T{P}^2 \\ \Rightarrow T{P}^2=O{P}^2-O{T}^2 \\ \Rightarrow TP=\sqrt{O{P}^2-O{T}^2} \\ \Rightarrow TP=\sqrt{{25}^2-7^2} \\ \Rightarrow TP=\sqrt{625-49} \\ \Rightarrow TP=\sqrt{576} \\ \Rightarrow TP=24\mathrm{cm} \end{gathered}$$
The length of the tangent to the circle is 24 cm.