At point A on the diameter AB of a circle of radius $\displaystyle 10$ cm , tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of $\displaystyle 16$ cm from A.

\(\displaystyle \mathrm{AP}=16 \mathrm{~cm}\) \(\displaystyle \therefore \mathrm{OP}=16-10=6 \mathrm{~cm}\) XY || CD \(\displaystyle \therefore \angle \mathrm{CPO}=90^{\circ}\) In right \(\displaystyle \Delta \mathrm{OPC}\), \[\begin{aligned} \mathrm{CP} & =\sqrt{(10)^{2}-(6)^{2}}=8 \mathrm{~cm} \\ \mathrm{CD} & =2 \times \mathrm{CP} \\ & =2 \times 8=16 \mathrm{~cm} \end{aligned} \]