TS EAMCET · Maths · Properties of Triangles
In \(\triangle \mathrm{ABC}\), if \(r_1+r_2=3 R, r_2+r_3=2 R\), then
- A ABC is a right-angled isosceles triangle
- B \(\mathrm{B}=\frac{\pi}{3}\)
- C \(\mathrm{A}=90^{\circ}, a \neq b \neq c\)
- D \(\mathrm{C}=90^{\circ}, a: b: c=2: 1: \sqrt{3}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{A}=90^{\circ}, a \neq b \neq c\)
Step-by-step Solution
Detailed explanation
\(r_1+r_2=3 \mathrm{R}\) \(\Rightarrow\left(\frac{\Delta}{s-a}\right)+\left(\frac{\Delta}{s-b}\right)=3\left(\frac{a b c}{4 \Delta}\right) \Rightarrow \frac{\Delta^2}{(s-a)(s-b)}=\frac{3 a b}{4}\)…
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