Question

In the given figure , point A is the centre and line AN = 10 cm. Line NM is the tangent at M. Determine the the radius of the circle, if MN = 5 cm

Answer 1

Construction: Join AM.


$$\begin{gathered} \angle \mathrm{AMN}=90°(\mathrm{Tangent}\mathrm{is}\mathrm{perpendicular}\mathrm{to}\mathrm{the}\mathrm{radius}) \\ \mathrm{So},\mathrm{in}∆\mathrm{AMN},\mathrm{we}\mathrm{have}: \\ \mathrm{AM}=\sqrt{{\mathrm{AN}}^2-{\mathrm{NM}}^2} \\ =\sqrt{{10}^2-5^2} \\ =\sqrt{100-25} \\ =\sqrt{75} \\ =5\sqrt{3}\mathrm{cm} \end{gathered}$$