TS EAMCET · Maths · Properties of Triangles
In \(\triangle \mathrm{ABC}\), if \(\mathrm{a}=7, \mathrm{~b}=8\) and \(\mathrm{c}=9\) then \(\frac{1}{\mathrm{r}_1^2}+\frac{1}{\mathrm{r}_2^2}+\frac{1}{\mathrm{r}_3^2}=\)
- A \(\frac{97}{360}\)
- B \(\frac{5}{72}\)
- C \(\frac{169}{360}\)
- D \(\frac{67}{72}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{72}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} a=7, b=8, c=9 \\ & \frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=\left(\frac{s-a}{\Delta}\right)^2+\left(\frac{s-b}{\Delta}\right)^2+\left(\frac{s-c}{\Delta}\right)^2 \\ & =\frac{(s-a)^2+(s-b)^2+(s-c)^2}{\Delta^2} \\ & =\frac{5^2+4^2+3^2}{12(5 \cdot…
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