CIRCLE
of two tangents drawn from
an external point to a circle are equal.
Q. PA and PB are tangents from an external point P to a circle
with circle O. LN touches the circle at M.
prove that PL + LM = PN + MN.
A
O
B
P
L
M
N
To Prove :
PL
+
LM
=
PN
+
MN
Proof :
PA
=
PB
…(i)
LA
=
LM
…(ii)
MN
=
NB
…(iii)
(Length of two tangents
from external point to
circle are equal)
PA
=
PB
[From (i)]
∴
PL
+
LA
=
PN
+
NB
[A-L-P, B-N-P]
∴
PL
+
LM
=
PN
+
MN
[From (ii) and (iii)]
We know, tangents drawn from an external point to a circle are equal in length.
Consider point P
What can you say about PA and PB?
They are tangents from external point P
Consider point L
LA and LM are tangents from external point L
Consider point N
MN and NB are tangents from external point N