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Standard X

Mathematics

Lengths of Tangents Drawn from External Point

In Fig. 8.64,...

Question

In Fig. 8.64, 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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Solution

PA = PB [TANGENTS DRAWN FROM AN EXTERNAL POINT TO A CIRCLE ARE EQUAL IN LENGTH]

PL + AL = PN + BN [P-L-A, AND P-N-B]

AL = ML & BN = MN [SAME REASON AS 1]

Thus, PL=ML [FROM 2 AND 3]

Hence, proved.

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In Fig. 8.64, 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.

PA = PB [TANGENTS DRAWN FROM AN EXTERNAL POINT TO A CIRCLE ARE EQUAL IN LENGTH] PL + AL = PN + BN [P-L-A, AND P-N-B] AL = ML & BN = MN [SAME REASON AS 1] Thus, PL=ML [FROM 2 AND 3] Hence, proved.

PA = PB [TANGENTS DRAWN FROM AN EXTERNAL POINT TO A CIRCLE ARE EQUAL IN LENGTH]

PL + AL = PN + BN [P-L-A, AND P-N-B]

AL = ML & BN = MN [SAME REASON AS 1]

Thus, PL=ML [FROM 2 AND 3]

Hence, proved.