Question

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

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

Answer 1

Answer: (D)

$121$

Answer 2

We know, if $T$ is any point on the circle, then
$PA \cdot PB = PT^2$
$\therefore PT = \sqrt {3^2 + 11^2 - 9 }$
$\sqrt{130 -9}$
$= \sqrt{121}$
$\therefore PA \cdot PB =(\sqrt{121})^2 = 121$