AP EAMCET · Maths · Straight Lines
Let origin be the centroid of an equilateral triangle \(\mathrm{ABC}\) and one of its sides be along the straight line \(x+y=3\). If \(\mathrm{R}\) and \(\mathrm{r}\) are its circum radius and inradius respectively, then \(\mathrm{R}+\mathrm{r}=\)
- A \(2 \sqrt{2}\)
- B \(\frac{9}{\sqrt{2}}\)
- C \(7 \sqrt{2}\)
- D \(\frac{3}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{9}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Given that one of the sides of the equilateral triangle be along the straight line \(x+y=3\) And we know in an equilateral triangle each side have an angle \(60^{\circ}\). \(\therefore \angle \mathrm{OBM}=\frac{60^{\circ}}{2}=30^{\circ}\) From the figure, \(r=\mathrm{OM}=\)…
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