Question

In the given figure, $PA$ and $PB$ are tangents from an external point $P$ to a circle with center $O$. $LN$ touches the circle at $M$. Prove that $PL+LM=PN+MN$.

Answer 1

From figure ,

Tangent drawn from outside point to circle at two points have equal length.

i.e. $PA=PB$

$\Rightarrow PL+LA=PN+NB$

$\Rightarrow PL+LM=PN+NM$ $\{\because LA=LM\because NB=NM\}$