AP EAMCET · Maths · Properties of Triangles
In a triangle \(A B C\), if \(\left(r_1-r_3\right)\left(r_1-r_2\right)-2 r_2 r_3=0\), then \(a^2-b^2=\)
- A \(c^2+\frac{b^2}{4}\)
- B \(c^2\)
- C abc
- D \(\frac{b+a}{c}\)
Answer & Solution
Correct Answer
(B) \(c^2\)
Step-by-step Solution
Detailed explanation
\( \left(r_1-r_3\right)\left(r_1-r_2\right) = 2 r_2 r_3 \) \( \left(\frac{S}{s-a} - \frac{S}{s-c}\right) \left(\frac{S}{s-a} - \frac{S}{s-b}\right) = 2 \frac{S}{s-b} \frac{S}{s-c} \) \( \frac{(a-c)}{(s-a)(s-c)} \frac{(a-b)}{(s-a)(s-b)} = \frac{2}{(s-b)(s-c)} \)…
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