Question

There are two concentric circles given. The radius of the bigger circle is 37 cm and
a 70 cm long chord of that circle touches the smaller circle. Find the radius of the
smaller circle.​

Answer 1

$\textbf{Given:}$

$\textsf{There are two concentric circles}$

$\textsf{The radius of the bigger circle is 37 cm and a 70 cm long}$

$\textsf{chord of that circle touches the smaller circle}$

$\textbf{To find:}$

$\textsf{Radius of the circle}$

$\textbf{Solution:}$

$\textsf{Let O be the centre of the circle}$

$\textsf{Let AB be the chord of length 70 cm}$

$\mathsf{Draw\;OC\;\perp\;AB}$

$\mathsf{Then,\;AC=BC=35}$

$\mathsf{In\;right\;\triangle\;OCB}$

$\mathsf{OB^2=OC^2+BC^2}$

$\mathsf{37^2=OC^2+35^2}$

$\mathsf{OC^2=37^2-35^2}$

$\mathsf{OC^2=(37-35)(37+35)}$

$\mathsf{OC^2=(2)(72)}$

$\mathsf{OC^2=144}$

$\mathsf{OC=\sqrt{144}}$

$\implies\boxed{\mathsf{OC=12\;cm}}$

$\textbf{Answer:}$

$\textsf{Radius of the smaller circle is 12 cm}$

Answer 2

$\textbf\red{Given:}$

$\textsf{There are two concentric circles}$

$\textsf{The radius of the bigger circle is 37 cm and a 70 cm long}$

$\textsf{chord of that circle touches the smaller circle}$

$\textbf\red{To find:}$

$\textsf{Radius of the circle}$

$\textbf\red{Solution:}$

$\textsf{Let O be the centre of the circle}$

$\textsf{Let AB be the chord of length 70 cm}$

$\mathsf{Draw\;OC\;\perp\;AB}$

$\mathsf{Then,\;AC=BC=35}$

$\mathsf{In\;right\;\triangle\;OCB}$

$\mathsf{OB^2=OC^2+BC^2}$

$\mathsf{37^2=OC^2+35^2}$

$\mathsf{OC^2=37^2-35^2}$

$\mathsf{OC^2=(37-35)(37+35)}$

$\mathsf{OC^2=(2)(72)}$

$\mathsf{OC^2=144}$

$\mathsf{OC=\sqrt{144}}$

$\implies\boxed{\mathsf{OC=12\;cm}}$

$\textbf{Answer:}$

$\textsf{Radius of the smaller circle is 12 cm}$