If in a triangle, a ^2 C 2 +c ^2 A 2 =3 b 2 , then its sides will… - Vidyadip

MCQ

If in a triangle, $a \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$, then its sides will be in

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A. P.
B
G. P.
C
H. P.
D
A.G.P.

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Answer

Correct option: A.

A. P.

(A) $a \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$
$\therefore \quad a \frac{s(s-c)}{a b}+c \frac{s(s-a)}{b c}=\frac{3 b}{2}$
$\begin{array}{l}\therefore 2 s(s-c+s-a)=3 b^2 \\ \therefore 2 s(b)=3 b^2 \Rightarrow 2 s=3 b \Rightarrow a+b+c=3 b \\ \therefore a+c=2 b \Rightarrow a, b, c \text { are in A.P. }\end{array}$

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