MHT CET · Maths · Properties of Triangles
In a triangle ABC , with usual notations , \(\tan \left(\frac{\mathrm{A}}{2}\right)=\frac{5}{6}, \tan \left(\frac{\mathrm{C}}{2}\right)=\frac{2}{5}\), then
- A \(\mathrm{a}, \mathrm{c}, \mathrm{b}\) are in A.P.
- B \(\mathrm{b}, \mathrm{a}, \mathrm{c}\) are in A.P.
- C \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are in A.P.
- D \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are in G.P.
Answer & Solution
Correct Answer
(C) \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are in A.P.
Step-by-step Solution
Detailed explanation
\(s-a = \frac{r}{\tan \left(\frac{\mathrm{A}}{2}\right)} = \frac{r}{5/6} = \frac{6r}{5}\) \(s-c = \frac{r}{\tan \left(\frac{\mathrm{C}}{2}\right)} = \frac{r}{2/5} = \frac{5r}{2}\)
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