Question

A chord of length 30cm is drawn at a distance of 8cm from the centre of a circle find the radius of a circle.

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{chord}\mathrm{AB}=30\mathrm{cm} \\ \mathrm{and}\mathrm{distance}\mathrm{of}\text{the}\mathrm{chord}\mathrm{from}\text{the}\mathrm{centre}\mathrm{O}=8\mathrm{cm} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{perpendicular}\mathrm{from}\mathrm{the}\mathrm{centre}\mathrm{on}\text{a}\mathrm{chord}\mathrm{of}\text{a}\mathrm{circle}\mathrm{bisects}\mathrm{the}\mathrm{chord}. \\ \therefore \mathrm{AM}=\mathrm{BM}=\frac{\mathrm{AB}}{2}=\frac{30}{2}=15\mathrm{cm} \\ \mathrm{Now}\mathrm{in}\mathrm{right}\mathrm{triangle},\mathrm{AMO}, \\ \mathrm{AO}=\sqrt{{\mathrm{AM}}^2+{\mathrm{MO}}^2} \\ =\sqrt{{15}^2+8^2} \\ =\sqrt{225+64} \\ =\sqrt{289} \\ =17\mathrm{cm} \\ \therefore \text{R}\mathrm{adius}\mathrm{of}\text{the}\mathrm{circle}=17\mathrm{cm}. \end{gathered}$$