question_answer

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    [SSC (CGL) 2012]

A) 5.5 cm             

B) 5 cm  

C) 4 cm                            

D) 4.5 cm

Correct Answer: B

Solution :

Let the radius of circle be r.

From figure,

\[PA\times PB=PQ\times PR\]

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

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

\[\Rightarrow \]               \[r=5\,\,cm\]