Question

Find the ratio of areas of incircle and circumcircle of an equilateral triangle .

ans. - 1 : 2

Please solve and post the figure also... ​

Answer 1

Answer:

$\huge\colorbox{yellow}{Answer\:-}$

$For \: an \: equilateral \: triangle \\ s = \frac{a + b + c}{2} = \frac{3a}{2}$

$and\:Δ = \frac{ \sqrt{3} }{4} {a}^{2}$

${r}^{2} = ( \frac{Δ}{s})^{2} = \frac{1}{12} {a}^{2}$

${R}^{2} = {( \frac{ {abc}^{2} }{4Δ} })^{2} = \frac{1}{3} {a}^{2}$

$\frac{Area\:of\:Circumcircle}{Area\:of\:Incircle} = \frac{\pi \: R ^{2} }{\pi \: r ^{2} } = \frac{ {a}^{2} }{3} \times \frac{12}{ {a}^{2} } = 4$

$\boxed{\pink{ = > 4:1}}$

$\huge\colorbox{yellow}{Thank\:You}$

Answer 2

Explanation:

answer for the following questions is 4:1