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  • In an equilateral triangle whose sides are 10 cm, then the ratio of the area of circumcircle and incircle isOption: 1 2:1<div class='qn

In an equilateral triangle whose sides are 10 cm, then the ratio of the area of circumcircle and incircle is

Option: 1

2:1


Option: 2

4:1


Option: 3

1:1


Option: 4

None of these


Answers (1)

best_answer

The circumradius of an equilateral triangle is  \mathrm{\mathbf{R}=\frac{a}{\sqrt3}}

The inradius of a triangle = Area of triangle/ Semi perimeter of triangle (Applicable for all triangles)

The inradius of an equilateral triangle is given by r, then

 \mathrm{r}=\frac{\sqrt3 a^2}{\mathrm{6a}}=\frac{a}{2\sqrt3}

\frac{\mathbf R}{r}=2

Hence, the ratios of area will be 4:1

 

Posted by

himanshu.meshram

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