Question

A point P is 26 cm away from the centre of a circle and the length of the tangent drawn from P to the circle is 24 cm. The radius of the circle is


(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 14 cm

Answer 1

(b) 10 cm
Given, point P is 26 cm away from the centre of a circle and the length of the tangent drawn from P to the circle is 24 cm. The centre of the circle is O.
The tangent at any point of a circle is perpendicular to the radius at the point of contact.
$$\begin{gathered} \therefore OT\perp PT \\ \therefore O{T}^2=O{P}^2-P{T}^2 \\ \Rightarrow O{T}^2={\left(26\right)}^2-{\left(24\right)}^2 \\ \Rightarrow O{T}^2=676-576 \\ \Rightarrow O{T}^2=100 \\ \Rightarrow OT=\sqrt{100} \\ \Rightarrow OT=10\mathrm{cm} \\ \therefore \mathrm{Radius}\mathrm{}\mathrm{of}\mathrm{}\mathrm{the}\mathrm{}\mathrm{circle}\mathrm{}\mathrm{is}10\mathrm{cm}. \end{gathered}$$