TS EAMCET · Maths · Properties of Triangles
If the angles of a \(\triangle A B C\) are in \(\mathrm{AP}\), then
- A \(c^2=a^2+b^2-a b\)
- B \(a^2=b^2+c^2-a c\)
- C \(b^2=a^2+c^2-a c\)
- D \(b^2=a^2+c^2\)
Answer & Solution
Correct Answer
(C) \(b^2=a^2+c^2-a c\)
Step-by-step Solution
Detailed explanation
Let the angle of \(\triangle A B C\), be \((a-d), a,(a+d)\) So, \(\quad a-d+a+a+d=180^{\circ} \Rightarrow a=60^{\circ}\) \(\begin{aligned} \cos B & =\frac{a^2+c^2-b^2}{2 a c} \\ \Rightarrow \quad \frac{1}{2} & =\frac{a^2+c^2-b^2}{2 a c} \Rightarrow b^2=a^2+c^2-a c\end{aligned}\)
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