In the figure, PA and PB are the tangents to the circle with centre O from a point P outside it LN touches it at M

To prove : PL + LM = PN + MN
Prove : PA and PB are tangents to the circle from P
PA = PB
Similarly from L, LA and LM are tangents
LA = LM
Similarly NB = NM
Now PA = PB => PL + LA = PN + NB
PL + LM = PN + NM
Hence proved.

In the figure, PA and PB are the tangents to the circle with centre O from a point P outside it LN touches it at M

To prove : PL + LM = PN + MN

Prove : PA and PB are tangents to the circle from P

PA = PB

Similarly from L, LA and LM are tangents

LA = LM

Similarly NB = NM

Now PA = PB => PL + LA = PN + NB

PL + LM = PN + NM

Hence proved.