AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), if \(A, B, C\) are in arithmetic progression, \(\Delta=\frac{\sqrt{3}}{2}\) and \(r_1 r_2=r_3 r\), then \(R=\)
- A \(\sqrt{3}\)
- B 2
- C 1
- D \(\sqrt{2}\)
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\begin{aligned} & A, B, C \text { are in AP, } r_1 r_2=r_3 r \\ & \Rightarrow \frac{\Delta}{(s-a)} \cdot \frac{\Delta}{(s-b)}=\frac{\Delta}{(s-c)} \cdot \frac{\Delta}{s} \\ & \Rightarrow \frac{(s-a)(s-b)}{s(s-c)}=1 \Rightarrow \tan ^2 \frac{C}{2}=1 \\ & C=90^{\circ},…
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