Question

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

Answer 1

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Answer 2

Answer:

We have to prove that PL+LM =PN+MN  ,where PA and PB are tangents from external point P to a circle with centre O . LN touches the circle at M.

• Use the property of tangents

Step-by-step explanation:

From the property of tangents we know that the length of two tangents drawn from an external point will we be equal. Hence we have,

PA=PB

PL+LA=PN+NB……(1)

Again from the same property of tangents we have,

LA=LM (where L is the common external point for tangents LA and LM )

NB=MN (where N is the common external point for tangents NB and MN )

Substituting LM and MN in place of LA and NB in equation (1), we have PL+LM=PN+MN