Two concentric circles are of radii $\displaystyle 5$ cm and $\displaystyle 3$ cm. Find the length of the chord of the larger circle which touches the smaller circle.

AB is the chord of larger circle touching the smaller circle at P. \[\mathrm{OA}=5 \mathrm{~cm}, \mathrm{OP}=3 \mathrm{~cm} \] To find AB \(\displaystyle \mathrm{OP} \perp \mathrm{AB}\) (radius ⟂ tangent) AB is the chord of larger circle and \(\displaystyle \mathrm{OP} \perp \mathrm{AB}\) \[\therefore \mathrm{AP}=\mathrm{PB} \] In right-angled \(\displaystyle \triangle \mathrm{AOP}, \mathrm{AP}^{2}=5^{2}-3^{2}=16\) \[\text { AP }=4 \mathrm{~cm} \] \(\displaystyle \therefore \mathrm{AB}=2 \mathrm{AP}=8 \mathrm{~cm}\)