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

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  1. 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
    RD Sharma Class 10 Textbook PDF Chapter 10 Circles
    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.

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