AP EAMCET · Maths · Properties of Triangles
In a triangle ABC , if \((a-b)(s-c)=(b-c)(s-a)\), then \(r_1+r_3=\)
- A \(r_2-r_3\)
- B \(3 r_2\)
- C \(2 r_2\)
- D \(3\left(r_1+r_2\right)\)
Answer & Solution
Correct Answer
(C) \(2 r_2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { In } \triangle A B C,(a-b)(s-c)=(b-c)(s-a) \\ \Rightarrow & \{(s-b)-(s-a)\}(s-c)=\{(s-c)-(s-b)\}(s-a) \\ \Rightarrow & \left(\frac{\Delta}{r_2}-\frac{\Delta}{r_1}\right)\left(\frac{\Delta}{r_3}\right)=\left(\frac{\Delta}{r_3}-\frac{\Delta}{r_2}\right)\le…
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