Quantitative Aptitude Ques 1823

Question: P is a point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersects the circle at points A and B in such a way that PA =9 cm and AB= 7 cm. The radius of the circle is

Options:

A) 5.5 cm

B) 5 cm

C) 4 cm

D) 4.5 cm

Show Answer

Answer:

Correct Answer: B

Solution:

  • Let the radius of circle be r. From figure, $ PA\times PB=PQ\times PR $

$ \Rightarrow $ $ 9\times (9+7)=(13-r)(13+r) $

$ \Rightarrow $ $ 169-r^{2}=144 $
$ \Rightarrow $ $ r^{2}=25 $

$ \Rightarrow $ $ r=5cm $

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