11.23. On one side of an acute angle, points $A$ and $B$ are given. Construct a point $C$ on the other side of the angle from which the segment $A B$ is seen at the largest angle.
11.23. Let $O$ be the vertex of the given angle. Point $C$ is the point of tangency of the side of the angle with a circle passing through points $A$ and $B$, i.e., $O C^{2}=O A \cdot O B$. To find the length of the segment $O C$, it is sufficient to draw a tangent to any circle passing through points $A$ and $B$.