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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