1.22. An equilateral triangle has an inscribed circle. Three small circles are tangent to this circle and the sides of the triangle. Find the side of the triangle if the radius of the small circle is $r$.

保留源文本的换行和格式，直接输出翻译结果。
1.22. Let $a$ be the side of a triangle, $R$ be the radius of the inscribed circle; then $R=\frac{a \sqrt{3}}{6}$.

Draw radii $O M$ and $O_{1} K$ to the points of tangency (Fig. 1.20). From the similarity of triangles $A O M$ and $A O_{1} K$,

we have $\frac{R}{r}=\frac{A O}{A O-R-r}$.

From this, considering that

![](https://cdn.mathpix.com/cropped/2024_05_21_1e3d8d2f6605ac23e2a5g-424.jpg?height=567&width=654&top_left_y=109&top_left_x=500)

Fig. 1.20 $A O=\frac{a \sqrt{3}}{3}$, we get

$$
\frac{a \sqrt{3}}{6 r}=\frac{a \sqrt{3}}{3\left(\frac{a \sqrt{3}}{3}-\frac{a \sqrt{3}}{6}-r\right)}, \text { or } \frac{a \sqrt{3}}{6}-r=2 r
$$

i.e., $a=6 r \sqrt{3}$.

Answer: $6 r \sqrt{3}$.