The angular magnitude of arc $A B$ is $\alpha<90^{\circ}$. On the extension of radius $O A$, a segment $A C$ equal to chord $A B$ is laid out, and point $C$ is connected to $B$. Find the angle $A C B$.
Apply the exterior angle theorem of a triangle.

## Solution

VAB is the exterior angle of the isosceles triangle $CAB$ and equals $90^{\circ} - \alpha / 2, \angle ACB = 1 / 2 \angle BAO = 45^{\circ} - \alpha / 4$.

![](https://cdn.mathpix.com/cropped/2024_05_06_7041536e9c9bacd5befeg-61.jpg?height=457&width=698&top_left_y=1255&top_left_x=680)

Answer

$45^{\circ} - \alpha / 4$.