A1. Each of the equilateral triangles $ABC$ and $DEF$ with side length 1 is divided into congruent equilateral triangles, in which circles are inscribed, as shown in the figure. What is the ratio of the areas between the shaded part of triangle $ABC$ and the shaded part of triangle $DEF$?
(A) $\frac{9}{16}$
(B) $\frac{3}{4}$
(C) 1
(D) $\frac{4}{3}$
(E) $\frac{16}{9}$

![](https://cdn.mathpix.com/cropped/2024_06_07_4050f14f84cf4f327f67g-04.jpg?height=440&width=688&top_left_y=768&top_left_x=1209)
A1. The ratio of the area of a triangle covered by its inscribed circle is $\frac{\pi \sqrt{3}}{9}$. In triangle $ABC$, each of the nine congruent triangles has a shaded area ratio of $\frac{\pi \sqrt{3}}{9}$, so triangle $ABC$ also has a shaded area ratio of $\frac{\pi \sqrt{3}}{9}$. The same applies to triangle $DEF$. Therefore, the ratios of the shaded areas are equal.