1.2. $A B$ is the diameter of a unit circle with center at point $O$. $C$ and $D$ are points on the circle such that $A C$ and $B D$ intersect inside the circle at point $Q$ and $\angle A Q B = 2 \angle C O D$. Find the distance from $O$ to the line $C D$.
1.2. Answer: $\frac{\sqrt{3}}{2}$.

![](https://cdn.mathpix.com/cropped/2024_06_04_b9e7a1c03f5c15132d5ag-18.jpg?height=60&width=1945&top_left_y=1763&top_left_x=61)
$\angle C O D=60^{\circ}$. Then $\triangle C O D$ is an equilateral triangle with side length 1, and the distance from $O$ to $C D$ is its height, which is $\frac{\sqrt{3}}{2}$.