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AP EAMCET · Maths · Properties of Triangles

In \(\triangle \mathrm{ABC}\), if \(\left(r_2-r_1\right)\left(r_3-r_{1}\right)=2 r_2 r_3\) then \(2(r+R)=\)

  1. A \(a+b\)
  2. B \(c+a\)
  3. C \(\quad 2 \sqrt{2} R \cos \left(\frac{C-A}{2}\right)\)
  4. D \(2 \sqrt{2} R \cos \left(\frac{B-C}{2}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \sqrt{2} R \cos \left(\frac{B-C}{2}\right)\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {Given that }\left(r_2-r_1\right)\left(r_3-r_1\right)=2 r_2 r_3 \\ & \Rightarrow\left(1-\frac{r_1}{r_2}\right)\left(1-\frac{r_1}{r_3}\right)=2 \\ &…