A circular plate with a weight of $P=1 \mathrm{~kg}$ is supported at three points along its circumference, which form an isosceles triangle. The vertex angle of this triangle is $\alpha=30^{\circ}$. What load rests on each support point?
The force $P$ acting at point $O$ is decomposed into components $x$ acting at point $A$ and $(P-x)$ acting at point $D$; thus,

$$
x \cdot \overline{A O}=(P-x) \overline{O D}
$$

where

$$
\begin{gathered}
\overline{O D}=\overline{O B} \cdot \cos \alpha=\overline{A O} \cdot \cos \alpha \\
x \overline{A O}=(P-x) \cdot \overline{A O} \cos \alpha \\
x=\frac{P \cos \alpha}{1+\cos \alpha}=\frac{\frac{1}{2} \sqrt{3}}{1+\frac{1}{2} \sqrt{3}}=2 \sqrt{3}-3=0.46411 \text{ kg}
\end{gathered}
$$

The force $(1-x)=2(2-\sqrt{3})$ acting at point $D$ is decomposed again into two components acting at points $B$ and $C$, which are equal, each being

$$
2-\sqrt{3}=0.26796 \text{ kg}
$$

(Zoltán Gádor, Losonc.)