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

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#### Solution

Given

O is Centre of circle

PA and PB are tangents

We know that

The tangents drawn from external point to the circle are equal in length.

From point P, PA = PB

⇒ PL + AL = PN + NB …. (i)

From point L & N, AL = LM and MN = NB } …. Substitute in (i)

PL + Lm = PN + MN

⇒ Hence proved.

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