Answer

Theorem: Tangents drawn from an external point to a circle are equal.

Here, PA and PB are tangents from an external point P

⇒ PA = PB

⇒ PL + LA = PN + NB [1]

Also, LA and LM are tangents from an external point L

⇒ LA = LM [2]

MN and NB are tangents from an external point N

⇒ NB = MN [3]

Using [2] and [3] in [1], we get

⇒ PL + LM = PN + MN

Hence Proved!