Draw a circle passing through three points; Geometry of Technical Drawing

This is one of those magic tricks done with a compass and straight edge that has always tickled my senses and amazed the people I've shared it with.
And actually; it's geometry, not magic.

That is: To find the Center of a Circle Passing through Three Points Not in a Straight Line and to Draw the Circle.

That's a mouthful. So read and reread it until you understand it. Then try it. Use the picture below to help you lay it out. The three points cannot be on a straight line. Once you get comfortable it will only take a minute to do!

You'll need: Paper, pencil, straight edge, and a drafting compass. And, If these instructions turn your head inside out this link will sort you out.

Let A, B and C be the three points. Draw the lines AB and BC. Now Draw the lines EO and DO; these lines are perpendicular to AB and BC.
Draw line DO by setting your compass to a length just over half the distance of line BC. Now strike arcs from either end of the line (at points B and C) so that they intersect on either side of the line (at points D and O). Use your straight edge to draw the line thru the two arcs points on intersection. Line DO will be perpendicular to line BC. Do the same for the line AB, and create EO.

The intersection O (of lines DO and EO) is the center of the circle. OA, OB and OC are the radius required to draw the circle using a compass. A circle drawn this way will pass through ANY three points not on a line!