PA and PB are tangents from P to the circle with center O At point M, a tangent in - Maths - Circles

Question

PA and PB are tangents from P to the circle with center O At point
M, a tangent in drawn cutting PA at K and PB at N Prove that KN =
AK + BN

Geetika Sharma · Accepted Answer

Dear student,

following is the answer to your question:
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5693651c0608e%20png"
style="width: 242px; height: 215px;">
In the given figure,

PA = PB (length of tangent from an external point to a circle are
equal)
similarly, KA = KM and (1)
NB = NM (2)
adding (1) and (2) we get,
KA + NB = KM + NM
=> AK + NB = KN (since, KM + NM = KN)
Hence proved

PA and PB are tangents from P to the circle with center O. At point M, a tangent in drawn cutting PA at K and PB at N. Prove that KN = AK + BN.