Question

A line is drawn through the point $P(3,11)$ to cut the circle $x^2+y^2=9$ at $AandB$. Then $PA\mathit{.}PB$ is equal to

• A. $9$
• B. $121$
• C. $205$
• D. $139$

Answer 1

The correct option is B

$121$

Finding the value of :

From geometry, we know

$PA.PB={\left(PT\right)}^2$ where $PT$ is the length of the tangent from $P$ to the circle.

$\begin{array}{rcl}PA.PB& =& {\left(3\right)}^2+{\left(11\right)}^2–9\\ & =& 9+{\left(11\right)}^2-9\\ & =& {11}^2\\ & =& 121\end{array}$

Hence, the correct answer is option B.