Question

At one end A of a diameter AB of a circle of radius 5 cm , tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
(a) 4 cm (b) 5 cm (c) 6 cm (d) 8 cm

Answer 1

XY is the tangent to the circle with centre O.
CD is the chord.
OA = OB = OD = 5 cm (Radii)
PA = 8 cm
PO = 3 cm
In ∆POD,
$$\begin{gathered} {\mathrm{PD}}^2+{\mathrm{PO}}^2={\mathrm{OD}}^2 \\ \Rightarrow 3^2+{\mathrm{PD}}^2=5^2 \\ \Rightarrow {\mathrm{PD}}^2=25-9=16 \\ \Rightarrow \mathrm{PD}=4\mathrm{cm} \end{gathered}$$
Hence, CD = CP + PD = 4 + 4 = 8 cm
so, the correct answer is option (d).