Question

In the given figure, C is the centre of the circle. seg QT is a diameter CT = 13, CP = 5, find the length of chord RS.

Answer 1

Join RC and CS.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, RP = PS
In $△$RPC,
$$\begin{gathered} {\mathrm{RP}}^2+{\mathrm{PC}}^2={\mathrm{RC}}^2 \\ \Rightarrow {\mathrm{RP}}^2+5^2={13}^2 \\ \Rightarrow {\mathrm{RP}}^2=169-25=144 \\ \Rightarrow \mathrm{RP}=12\mathrm{cm} \end{gathered}$$
Thus, RP = PS = 12 cm
So, RS = RP + PS = 12 + 12 = 24 cm.