Question

$PA$ and $PB$ are tangents to a circle $S$ touching it at points $A$ and $B$, respectively. $C$ is a point on $S$ in between $A$ and $B$ as shown in the figure. $LCM$ is a tangent to $S$ intersecting $PA$ and $PB$ in points $L$ and $M$, respectively. Then the perimeter of the triangle $PLM$ depends on

• A. $A,B,C$ and $P$
• B. $P$ but not on $C$
• C. $P$ and $C$ only
• D. radius of $S$ only

Answer 1

Answer: (B)

Perimeter of $\Delta PLM=PL+LC+CM+MP$
$=PL+LA+BM+MP$
$=PA+PB$