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

A) 5.5 cm             

B) 5 cm

C) 4 cm                            

D) 4.5 cm.

Correct Answer: B

Solution :

From figure,

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

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

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

\[\Rightarrow \]   \[{{r}^{2}}=25\]\[\Rightarrow \]\[r=5\,cm\]