TS EAMCET · Maths · Properties of Triangles
In triangle \(A B C\), if \(b=6, c=7\) and \(\tan \frac{A}{2}=\frac{1}{\sqrt{6}}\), then the inradius of \(\triangle \mathrm{ABC}\) is
- A \(\sqrt{\frac{2}{3}}\)
- B \(\frac{2 \sqrt{6}}{9}\)
- C \(\frac{\sqrt{2}}{9}\)
- D \(\frac{2 \sqrt{6}}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \sqrt{6}}{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } b=6, c=7 \\ & \tan \frac{A}{2}=\frac{1}{\sqrt{6}} \\ & \cos A=\frac{1-\tan ^2 \frac{A}{2}}{1+\tan ^2 \frac{A}{2}}=\frac{1-\frac{1}{6}}{1+\frac{1}{6}}=\frac{5}{7} \\ & \cos A=\frac{b^2+c^2-a^2}{2 b c} \\ & \Rightarrow \frac{5}{7}=\frac{36+49-a^2}{2…
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