Question 33
Euclid has a tool called *cyclos* which allows him to do the following:
* Given three non-collinear marked points, draw the circle passing through them.
* Given two marked points, draw the circle with them as endpoints of a diameter.
* Mark any intersection points of two drawn circles or mark a new point on a drawn circle.
Show that given two marked points, Euclid can draw a circle centered at one of them and passing through the other, using only the cyclos.
* Given three non-collinear marked points, draw the circle passing through them.
* Given two marked points, draw the circle with them as endpoints of a diameter.
* Mark any intersection points of two drawn circles or mark a new point on a drawn circle.
Show that given two marked points, Euclid can draw a circle centered at one of them and passing through the other, using only the cyclos.