Question

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

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

Answer 1

The correct option is B $121$

From geometry we know $PA\cdot PB=(PT{)}^2$

where $PT$ is the length of the tangent from $P$ to the circle.

Hence $PA\cdot PB=(3{)}^2+(11{)}^2-9={11}^2=121$