Question

If radii of two concentric circles are 4 cm and 5 cm , then the length of each chord of one circle which is tangent to the other circle is
(a) 3 cm (b) 6 cm (c) 9 cm (d) 1 cm

Answer 1

Let the chord of one circle which tangent to the other be AB.
In ∆AOC,
$$\begin{gathered} {\mathrm{OC}}^2+{\mathrm{AC}}^2={\mathrm{OA}}^2 \\ \Rightarrow {\mathrm{AC}}^2={\mathrm{OA}}^2-{\mathrm{OC}}^2 \\ \Rightarrow {\mathrm{AC}}^2=5^2-4^2 \\ \Rightarrow {\mathrm{AC}}^2=25-16=9 \\ \Rightarrow \mathrm{AC}=3\mathrm{cm} \end{gathered}$$
thus, AB = AC + CB = 3 + 3 = 6 cm
Hence, the correct answer is option (b).