AP EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C,(a+b+c)(b+c-a)=\lambda b c\), then
- A \(\lambda < -6\)
- B \(\lambda>6\)
- C \(0 < \lambda < 4\)
- D \(\lambda>4\)
Answer & Solution
Correct Answer
(C) \(0 < \lambda < 4\)
Step-by-step Solution
Detailed explanation
\((a+b+c)(b+c-a)=\lambda b c\) \(((b+c)+a)((b+c)-a)=\lambda b c\) \((b+c)^2 - a^2=\lambda b c\) \(b^2+c^2+2bc-a^2=\lambda b c\) \( (b^2+c^2-a^2) + 2bc = \lambda bc \) From Law of Cosines, \(b^2+c^2-a^2 = 2bc \cos A\). \(2bc \cos A + 2bc = \lambda bc\) \(2 \cos A + 2 = \lambda\)…
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