At one end of a diameter PQ of a circle of radius 5 cm, tangent XPY is drawn to the circle.

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

Solution:

Consider the figure.

In right angled $\triangle \mathrm{OMB}$,

By pythagoras theorem.

$\mathrm{OB}^{2}=\mathrm{MB}^{2}+\mathrm{OM}^{2}$

$\Rightarrow 5^{2}=\mathrm{MB}^{2}+3^{2}$

$\Rightarrow 25-9=\mathrm{MB}^{2}$

$\Rightarrow 16=\mathrm{MB}^{2}$

 

$\Rightarrow 4=\mathrm{MB}$

Therefore, AM = 2MB = 2 × 4 = 8 cm.
Hence, the correct answer is option (d).

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