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TS EAMCET · Maths · Properties of Triangles

In any \(\triangle A B C, r_1 r_2+r_2 r_3+r_3 r_1\) is equal to

  1. A \(\frac{\Delta^2}{r^2}\)
  2. B \(\frac{\Delta}{r}\)
  3. C \(\frac{2 \Delta}{r}\)
  4. D \(\Delta^2\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\Delta^2}{r^2}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { In } \triangle A B C, \\ & =\frac{\Delta}{s-a} \cdot \frac{\Delta}{s-b}+\frac{\Delta}{s-b} \cdot \frac{r_1 r_2+r_2 r_3+r_3 r_1}{s-c}+\frac{\Delta}{s-c} \cdot \frac{\Delta}{s-a} \\ & =\frac{\Delta^2}{(s-a)(s-b)(s-c)}[s-c+s-a+s-b]\end{aligned}\)…