Question

In Fig. 10.60, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at A. Prove that PL + LM = PN + MN.

Answer 1

Explanation:

Given that PA and PB are tangents from an external point P to a circle with centre O.

Also, given that LN touches the circle at A.

To prove that : $\ {PL}+\ {LM}=\ {PN}+\ {MN}$

Since, we know that, the two tangents drawn from an external point to a circle are equal in length.

Hence, we have,

$P A=P B$

From the figure, we can see that L intersects the tangent PA and N intersects the tangent PB

Thus, we have,

$\ {PL}+\ {AL}=\ {PN}+\ {NB}$ -----------(1)

Let us apply the tangent property for the point L and N, we have,

$\ {AL}=\ {LM}$ and

$\ {MN}=\ {NB}$

Substituting these values in the equation (1), we get,

$\ {PL}+\ {LM}=\ {PN}+\ {MN}$

Hence proved.

Learn more:

(1) Prove that PL + LM = PN + MN.

brainly.in/question/6752417

(2) What is the answer of this question​

brainly.in/question/15827664