Let $ABC$ be an equilateral triangle with side length $a$. Let $R$ and $r$ denote the radii of the circumcircle and the incircle of triangle $ABC$ respectively. Then,as a function of $a$,the ratio $\frac{R}{r}$
- Astrictly increases
- Bstrictly decreases
- Cremains constant
- Dstrictly increases for $a < 1$ and strictly decreases for $a > 1$
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Similar Questions
In a $\triangle ABC$, if $a: b: c = 4: 5: 6$, then the ratio of the radius of its circumcircle to that of its incircle is:
In a $\triangle ABC$,which of the following formulae are correct?
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$
In $\triangle ABC$,find the value of $\frac{r_1-r}{a}+\frac{r_2-r}{b}$.
DifficultAP EAMCET 2023
View SolutionIn $\Delta ABC,$ the lengths of sides $AC$ and $AB$ are $12 \, cm$ and $5 \, cm,$ respectively. If the area of $\Delta ABC$ is $30 \, cm^{2}$ and $R$ and $r$ are respectively the radii of the circumcircle and incircle of $\Delta ABC,$ then the value of $2R + r$ (in $cm$) is equal to ....... .
DifficultJEE MAIN 2021
View SolutionIn a $\triangle ABC$,$2A + C = 300^{\circ}$. If the circumradius $R$ of the $\triangle ABC$ is eight times its inradius $r$,then $\sin \frac{C}{2} = $
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