AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), if \(a=3, b=4, c=6\), then \(\frac{\cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}}{\cot A+\cot B+\cot C}=\)
- A \(\frac{13}{61}\)
- B \(\frac{169}{61}\)
- C \(\frac{61}{169}\)
- D \(\frac{61}{13}\)
Answer & Solution
Correct Answer
(B) \(\frac{169}{61}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \cot \frac{A}{2}+\cot \frac{B}{2}+\cot & \frac{C}{2}=\frac{s(s-a)}{\Delta} \\ & \quad+\frac{s(s-b)}{\Delta}+\frac{s(s-c)}{\Delta} \\ & =\frac{S}{\Delta}[3 S-(a+b+c)] \\ & =\frac{S}{\Delta}(S)=\frac{S^2}{\Delta}=\frac{(a+b+c)^2}{4 \Delta}\end{aligned}\) Now,…
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