TS EAMCET · Maths · Properties of Triangles
Let the angles \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) of a triangle ABC be in arithmetic progression. If the exradii \(r_1, r_2, r_3\) of triangle ABC satisfy the condition \(r_3^2=r_1 r_2+r_2 r_3+r_3 r_1\), then \(b=\)
- A \(\frac{2 a}{\sqrt{3}}\)
- B \(\sqrt{2} a\)
- C \(\sqrt{3} a\)
- D a
Answer & Solution
Correct Answer
(C) \(\sqrt{3} a\)
Step-by-step Solution
Detailed explanation
\(A, B, C\) in AP \(\implies B=60^\circ\). \(r_3^2=r_1 r_2+r_2 r_3+r_3 r_1 \implies r_3^2 = s^2 \implies r_3 = s\). \(r_3 = \frac{\Delta}{s-c} \implies s = \frac{\Delta}{s-c} \implies s(s-c) = \Delta\). \(s^2(s-c)^2 = s(s-a)(s-b)(s-c) \implies s(s-c) = (s-a)(s-b)\).…
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