AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), if \(\frac{s-a}{11}=\frac{s-b}{12}=\frac{s-c}{13}\), then \(\tan ^2\left(\frac{A}{2}\right)+\tan ^2\left(\frac{C}{2}\right)=\)
- A \(\frac{290}{429}\)
- B \(\frac{290}{143}\)
- C \(\frac{143}{33}\)
- D \(\frac{113}{33}\)
Answer & Solution
Correct Answer
(A) \(\frac{290}{429}\)
Step-by-step Solution
Detailed explanation
Given that, \(\frac{s-a}{11}=\frac{s-b}{12}=\frac{s-c}{13}=k\) \[ \begin{aligned} & s-a=11 k \\ & s-b=12 k \\ & s-c=13 k \end{aligned} \] On adding, \[ \begin{aligned} 3 s-(a+b+c) & =36 k \\ 3 s-2 s & =36 k \\ s & =36 k \end{aligned} \quad[\text { as } a+b+c=2 s] \] Now,…
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