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AP EAMCET · Maths · Properties of Triangles

In \(\triangle \mathrm{ABC}\) if \(r_1=8, r_2=12\) and \(r_3=24\) then the ordered triple \((a, b, c)=\)

  1. A \((8,12,14)\)
  2. B \((12,16,20)\)
  3. C \((16,12,20)\)
  4. D \((16,20,12)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((12,16,20)\)

Step-by-step Solution

Detailed explanation

\(\frac{1}{r} = \frac{1}{8} + \frac{1}{12} + \frac{1}{24} = \frac{3+2+1}{24} = \frac{6}{24} = \frac{1}{4} \implies r=4\) \(\Delta = \sqrt{r r_1 r_2 r_3} = \sqrt{4 \cdot 8 \cdot 12 \cdot 24} = \sqrt{9216} = 96\) \(s = \frac{\Delta}{r} = \frac{96}{4} = 24\)…