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Byju's Answer
Standard XII
Mathematics
Angle between Pair of Straight Lines
The angles A,...
Question
The angles A, B, C of a ∆ABC are in AP and the sides a, b, c are in G.P. If a
2
+ c
2
= λb
2
, then λ = ____________.
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Solution
Since A, B, C are A.P
⇒ 2B = A + C
Since A + B + C =
π
(By angle sum property)
⇒ 3B =
π
i
.
e
B
=
π
3
.
.
.
1
also,
Since a, b, c are in g.p
⇒ b
2
= ac ....(2)
Using cosB =
a
2
+
c
2
-
b
2
2
a
c
i.e
cos
π
3
=
a
2
+
c
2
-
a
c
2
a
c
from (1) and (2).
⇒
1
2
=
a
2
+
c
2
-
a
c
2
a
c
⇒ ac = a
2
+ c
2
- ac
⇒ a
2
+ c
2
= 2ac
⇒ a
2
+ c
2
= 2b
2
from (2)
Hence
λ
= 2
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