Find the center of a circle using straight-edge and compass with given conditions. My geometry teacher challenged me to find a way to find the center of a given circle using only _**one circle**_ and _**four lines**_. No tangents either. I can't seem to find a way to do this, all I've found so far are different ways of finding the diameter of the circle with one line left. I have always get one line left to draw, and through my own constructions,there aren't any points that I could use to draw another straight line through the diameter to find the center. This is Euclidean Geometry by the way. A simpler version of the paragraph above is to simplify the construction of Book Three Proposition one in Euclidean Geometry so that the construction takes 4 straight lines and one circle.

It is actually not possible. My teacher said that after a little bit of thought, he thinks it is not possible.