Question

In the figure, PA and PB are two tangents to the circle with center O. One point M is on the circle, then prove that PL + LM = PN + MN.

Answer 1

Given :

PA and PB are two tangent of the circle. 

Line segment LN touches the circle at point M.

To prove:

PL + LM = PN + MN

Proof :

∴ Two tangents PA and PB drawn from point P.

So PA = PB

or PL + LA = PN + NB

Two tangents LA and LM are from point L

So LA = LM …(ii)

Similarly NB = NM .. .(iii)

From equation (i), (ii) and (iii) we get.

PL + LM = PN + NM.