AP EAMCET · Maths · Properties of Triangles
If \(s\) is the semi-perimeter of \(\triangle A B C\) and if \(\frac{s-a}{4}=\frac{s-b}{5}=\frac{s-c}{6}\), then \(\sum \sin ^2\left(\frac{A}{2}\right)=\)
- A \(\frac{74}{25}\)
- B \(\frac{25}{74}\)
- C \(\frac{74}{33}\)
- D \(\frac{25}{33}\)
Answer & Solution
Correct Answer
(D) \(\frac{25}{33}\)
Step-by-step Solution
Detailed explanation
Let \(\frac{s-a}{4}=\frac{s-b}{5}=\frac{s-c}{6}=k\) \(\Rightarrow b+c-a=8 k, a+c-b=10 k\) and \(a+b-c=12 k\) So, \(a+b+c=30 k \Rightarrow s=15 k, a=11 k, b=10 k\) and \(c=9 k\)…
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