In an equilateral triangle, the perpendicular bisectors, angle bisectors, and medians coincide, particularly their midpoints. The centroid divides the medians in the ratio 2:1, with the longer segment pointing towards the vertices.

Accordingly, the circumradius is exactly twice the inradius, and a ratio of 4 results between the circumcircle area and the incircle area.
## Task 4 - 080934

Given is an equilateral triangle $\triangle A B C$. Determine the ratio of the areas of the incircle and the circumcircle of this triangle to each other!