Using only a drafting triangle and a pencil it is possible to find the center of a circle.
How many times will you need to change the position of the drafting triangle to reach the goal? The initial placement is counted as the 1st change.
Explanations
4 times.
Place C, the right angle of the drafting triangle on the circumference, as is shown (1st change of the position). D and E, where triangle's legs cross the circumference, are the endpoints of a diameter. Draw it (2nd change).
Now get a second diameter the same way (3rd and 4th changes respectively).
The intersection of these two diameters is the center of the circle.
[After Boris A. Kordemsky. The Moscow Puzzles: 359 mathematical recreations. 1972]