Question

A line is drawn through the point $P(4,7)$ which cuts the circle $x^2+y^2=9$ at the points A and B. Then, $PA\cdot PB$ is equal to

• A. $74$
• B. $56$
• C. $53$
• D. $65$

Answer 1

Answer: (B)

$56$

$PA.PB=(PC{)}^2$ where $C$ is the point of contact of a tangent drawn to the circle from point $P$.

If the center of the circle is $O,\Delta POC$ forms a right-angled triangle where

$(PO{)}^2=(OC{)}^2+(PC{)}^2$

$\Rightarrow (4-0{)}^2+(7-0{)}^2=9+(PC{)}^2$

$\Rightarrow (PC{)}^2=16+49-9=56$

$\therefore PA.PB=56$