Question

Out of the two concentric circles, the radius of the outer circle is $ 5 \mathrm{cm}$ and the chord $ AC$ of length $ 8 \mathrm{cm}$ is a tangent to the inner circle. Find the radius of the inner circle.

Answer 1

The radius of the inner circle.

It is given that $AB=8\mathrm{cm},OA=5\mathrm{cm},OC\perp AB$

Apply Pythagoras theorem In the right triangle $OCA$:

$$\begin{gathered} O{C}^2+C{A}^2=O{A}^2 \\ \Rightarrow O{C}^2=5^2-4^2 \\ \Rightarrow O{C}^2=25-16 \\ \Rightarrow O{C}^2=9 \\ \therefore OC=3\mathrm{cm} \end{gathered}$$

Hence, the radius of the inner circle is $3\mathrm{cm}$.