TS EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C\), if \(a \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}\), then
- A \(2 b=a+c\)
- B \(b^2=a c\)
- C \(b^2=\frac{2 a c}{a+c}\)
- D \(a+b+c=1\)
Answer & Solution
Correct Answer
(A) \(2 b=a+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given, } a \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2} \\ & \Rightarrow a(1+\cos c)+c(1+\cos A)=3 b \\ & \Rightarrow a+c+(a \cos C+c \cos A)=3 b \\ & \Rightarrow(a+c)+b=3 b \Rightarrow a+c=2 b\end{aligned}\)
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