Question

In the following figure, point 'A' is the centre of the circle. Line MN is tangent at point M. If AN$=10$cm and MN$=5$cm, determine radius of the circle.

Answer 1

In $\Delta AMN$, $m\angle AMN={90}^{\circ }$

$\therefore A{N}^2=A{M}^2+M{N}^2$ (By Pythagoras theorem)

Given $AN=10cm,MN=5cm$

$\therefore {10}^2=A{M}^2+5^2$

$\Rightarrow A{M}^2={10}^2-5^2$

$\Rightarrow A{M}^2=100-25$

$\Rightarrow A{M}^2=75$

$\Rightarrow AM=\sqrt{75}$

$\Rightarrow AM=\sqrt{25\times 3}$

$\Rightarrow AM=5\sqrt{3}$

Thus the radius of the circle is $5\sqrt{3}cm$