AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), if \(r=3\) and \(R=5\) then \(\frac{1}{a b}+\frac{1}{b c}+\frac{1}{c a}=\)
- A \(\frac{1}{30}\)
- B \(\frac{12}{15}\)
- C \(\frac{1}{15}\)
- D \(\frac{5}{36}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{30}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca} = \frac{a+b+c}{abc} = \frac{2s}{4R\Delta} = \frac{2s}{4R(rs)} = \frac{1}{2Rr}\) \(\frac{1}{2(5)(3)} = \frac{1}{30}\)
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