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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