Question

At one end of a diameter PQ of a circle of radius 5 cm, tangent XPY is drawn to the circle. The length of chord AB parallel to XY and at a distance of 8 cm from P is

(a) 5 cm

(b) 6 cm

(c) 7 cm

(d) 8 cm

Answer 1

Consider the figure.
fIG

In right angled $∆\mathrm{OMB}$,

By pythagoras theorem.

$$\begin{gathered} {\mathrm{OB}}^2={\mathrm{MB}}^2+{\mathrm{OM}}^2 \\ \Rightarrow 5^2={\mathrm{MB}}^2+3^2 \\ \Rightarrow 25-9={\mathrm{MB}}^2 \\ \Rightarrow 16={\mathrm{MB}}^2 \\ \Rightarrow 4=\mathrm{MB} \end{gathered}$$
Therefore, AM = 2MB = 2 × 4 = 8 cm.
Hence, the correct answer is option (d).