7. If three points are randomly chosen on a circle, the probability that the triangle formed by these three points is an acute triangle is $\qquad$ .


7. $\frac{1}{4}$.

Let $\triangle A B C$ be any inscribed triangle in a circle with radius 1, and let the arc lengths opposite to $\angle A$ and $\angle B$ be $x$ and $y$, respectively. Then the arc length opposite to $\angle C$ is $2 \pi - x - y$.
For $\triangle A B C$, we have
$$
\left\{\begin{array}{l}
0 < x < 2 \pi, \\
0 < y < 2 \pi, \\
0 < 2 \pi - (x + y) < 2 \pi
\end{array}\right.
$$

The area of the region represented by this system of inequalities is
$$
S_{1} = 2 \pi^{2}.
$$

If $\triangle A B C$ is an acute triangle, then
$$
\left\{\begin{array}{l}
0 < x < \pi, \\
0 < y < \pi, \\
0 < 2 \pi - (x + y) < \pi.
\end{array}\right.
$$

The area of the region represented by this system of inequalities is
$$
S_{2} = \frac{\pi^{2}}{2}.
$$

Thus, the required probability is $\frac{S_{2}}{S_{1}} = \frac{1}{4}$.