AP EAMCET · Maths · Properties of Triangles
In triangle ABC, if \(\mathrm{a}=6, \mathrm{~b}=8\) and \(\mathrm{c}=10\), then \(\frac{2 \mathrm{r}_2 \mathrm{r}_3}{\mathrm{rr}_1}=\)
- A \(b+c\)
- B \(c+a\)
- C \(a+b\)
- D \(a+b+c\)
Answer & Solution
Correct Answer
(A) \(b+c\)
Step-by-step Solution
Detailed explanation
\(\frac{2 \mathrm{r}_2 \mathrm{r}_3}{\mathrm{rr}_1} = \frac{2 \left(\frac{\Delta}{s-b}\right) \left(\frac{\Delta}{s-c}\right)}{\left(\frac{\Delta}{s}\right) \left(\frac{\Delta}{s-a}\right)} = \frac{2s(s-a)}{(s-b)(s-c)}\) \(s = \frac{6+8+10}{2} = 12\) \(s-a = 12-6 = 6\)…
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