Question 23
Consider two points $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$ on the graph of the function $y=\frac{1}{x}$ such that $0\lt x_{1}\lt x_{2}$ and $|A B|=2 \cdot|O A|$ ($O$ is the reference point, i.e., $O(0,0)$). Let $C$ be the midpoint of the segment $A B$. Prove that the angle between the $x$-axis and the ray $O A$ is equal to three times the angle between $x$-axis and the ray $O C$.