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AP EAMCET · Maths · Properties of Triangles

In \(\triangle \mathrm{ABC}\), if \(r_1=3, r_2=10\) and \(r_3=15\), then \(\mathrm{R}=\)

  1. A \(5\)
  2. B \(12\)
  3. C \(\frac{13}{2}\)
  4. D \(13\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{13}{2}\)

Step-by-step Solution

Detailed explanation

\(\frac{1}{r} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}\) \(\frac{1}{r} = \frac{1}{3} + \frac{1}{10} + \frac{1}{15} = \frac{10+3+2}{30} = \frac{15}{30} = \frac{1}{2} \implies r=2\) \(R = \frac{r_1+r_2+r_3-r}{4}\) \(R = \frac{3+10+15-2}{4} = \frac{26}{4} = \frac{13}{2}\)