AP EAMCET · Maths · Properties of Triangles
If, in a \(\triangle A B C, \tan \frac{A}{2}=\frac{5}{6}\) and \(\tan \frac{C}{2}=\frac{2}{5}\), then \(a, b, c\) are such that :
- A \(b^2=a c\)
- B \(2 b=a+c\)
- C \(2 a c=b(a+c)\)
- D \(a+b=c\)
Answer & Solution
Correct Answer
(B) \(2 b=a+c\)
Step-by-step Solution
Detailed explanation
\(\because \quad \tan A=\frac{5}{6}\) and \(\tan C=\frac{2}{5}\) \(\therefore \quad \tan A \tan C=\frac{5}{6} \cdot \frac{2}{5}\) \(\Rightarrow \quad \frac{s-b}{s}=\frac{1}{3}\) \(\Rightarrow \quad 3 s-3 b=s\) \(\Rightarrow \quad 2 s=3 b\) \(\Rightarrow \quad a+c=2 b\)
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