How I can calculate the hand position on a clock background?
If you have a compass, the drawing kind, not the magnetic kind, you can create the intermediate locations for the hours.
https://youtu.be/2Vshz0kqZh4
The video above shows the process, but I was skeptical until I realized that it's a collection of overlapping equilateral triangles. Equilateral triangles have 60° in each vertex. You want to segment the 90° of the currently created locations (12, 3, 6, 9) into three pieces, 30° each. 90° - 60° = 30°
If you create an equilateral triangle with the base on the 3:00 line, for example, the 60° line of the triangle becomes the 1:00 position. If the triangle is created with the base on the 12:00 line, the triangle provides the 2:00 position.