Question

Two concentric circles are of radii $8cm$ and $5cm$.Find the length of the chords of the larger circle which touches the smaller circle.

Answer 1

As perpendicular from centre bisects the chord

$\Rightarrow QR=PR$

In $\Delta ORQ$ by Pythagoras theorem,

$O{Q}^2=O{R}^2+R{Q}^2$

$\Rightarrow QR=\sqrt{64-25}=\sqrt{39}$

Also,

$PQ=2RQ$

$\Rightarrow PQ=2\sqrt{39}$cm.