When we bisect the equilateral triangle, the bisector will be equal to the radius of the bigger circle. Here let us consider radius of the bigger circle as 2.
By forming the 30-60-90 triangle, you can calculate that the radius of the smaller circle as 1.
So, the area of the bigger circle is 4π
So, the area of the smaller circle is π
So, the ratio of two circles is 1:4
_________________

not certainly this way. Point out another way.......Assume that you don,t know what will be the answer, and then find out it in your own way.
_________________

the base of the equilateral triangle to the center of the small circle=1/3 the height of the triangle
the vertex of any side of the triangle( which touches the circumference of the bigger circle) to the center of the bigger circle (which also coincides with the center of the smaller circle)= 2/3 the height of the triangle
radius of smaller circle=1/3
radius of bigger circle=2/3
small circle area:bigger circle area=(1/3)^2:(2/3)^2=1:4

Here's a similar question to practice with: https://greprepclub.com/forum/in-the-ab ... -9519.html

Cheers,
Brent
_________________

Many Many Many Thanks
_________________

huda
Ratio of two circles what?

Radius: 2:1
Area: 4:1
Circumference: 2:1

[NOTE: All the above ratios are bigger circle to smaller circle]
_________________