Question

If $C$ is the mid - point of $AB$ and $P$ is any point outside $AB$, then

• A. $PA+PB=PC$
• B. $PA+PB+2PC=0$
• C. $PA+PB-2PC=0$
• D. $PA+PB+PC=0$

Answer 1

The correct option is C

$PA+PB-2PC=0$

Explanation for the correct option:

Finding the value:

Given,$C$ is the mid point of $AB$

$P$ is any point outside $AB$

$PA=PC+CA$

$PB=PC+CB$

$PA+PB=2PC+\left(CA+CB\right)=2PC$ $\left(\because CA=-CB\right)$

$PA+PB-2PC=0$

Hence, option C is correct.