Question

In the given fig. PA and PB are tangents to the circle. Prove that: KN = AK + BN.

Answer 1

SOLUTION :
GIVEN:
PA & PB are tangents to the circle.

We know that the tangents drawn from an external point to a circle are equal in length.

PA = PB       [ From P ]..........(1)
KA = KM       [ From K ]...........(2)
NB = NM       [ From N ]...........( 3)

On adding equation 2 and 3,
KA + NB = KM + NM
AK + BN = KM + NM
AK + BN = KN        [ KM + NM = KN]

Hence, proved.

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Answer 2

Answer:

GIVEN:

PA & PB are tangents to the circle.

We know that the tangents drawn from an external point to a circle are equal in length.

PA = PB       [ From P ]..........(1)

KA = KM       [ From K ]...........(2)

NB = NM       [ From N ]...........( 3)

On adding equation 2 and 3,

KA + NB = KM + NM

AK + BN = KM + NM

AK + BN = KN        [ KM + NM = KN]

Hence, proved.