Question

What is the ratio of the areas of circles inscribed and circumscribed in a
equilateral triangle ?
(a) 1:2
(6) 1:3
(c) 1:4
(d) 1:9​

Answer 1

Answer:

Let the side of equilateral triagle be 2a.

The radius of inscribed circle

= a*tan 30=a/(3)^0*5

Area of inscribed circle A1=( 22/7)a^2/3

=22a^2/21.

The radius of circumscribed circle = (a^2+a^2/3)^0.5= 2a/(3^0.5)

Area of circumscribed circle A2 =

22/7*(4a^2/3)=88a^2/21

Side of the triangle inscribed in Circle A1=a and its area A3=0.5*a*(a/2)*3^0.5/2

=(a^2/8)*3^0.5

Ratio A2/A3 = (88/21)*8/3^0.5=704/(21*3^0.5)

Answer 2

Answer:

$(c) \: 1: 4.$

Step-by-step explanation:

$Ratio \: of \: area \: = \: The \: square \: of \: ratio \: of \: length \\ = \: {(1:2)}^{2} \\ = \: \frac{(1}{2)} {}^{2} \\ = \: \frac{1}{4} \\ = \: \: 1:4.$

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