The ratio of the areas of the circumcircle and the incircle

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The ratio of the areas of the circumcircle and the incircle of an equilateral triangle is

For the equilateral triangle of side a,

In radius =	a
	2√3

Circum-radius =	a
	√3

∴ Required ratio =		a		²	: π		a		²
		√3					2√3

=	1	:	1	= 4 : 1
	3		12