Draw the largest circle in an equilateral triangle, then draw the largest equilateral triangle in this circle, and write the area ratio of the two triangles?

Let the length of an equilateral triangle be a, draw the largest circle in the equilateral triangle as its inscribed circle, and the radius r=a/3.

The largest equilateral triangle in this circle is the triangle inscribed in the circle, and the relationship between its side length and the radius of the circle is side length = 2/3 * R.

So the side length of a small triangle is (a/3)÷(2/3)=a/2.

The side length of a small triangle is 1/2 that of a large triangle.

Small triangle area: large triangle area = 1: 4.

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