JavaScript and Flash Required to view Circles Are Awesome
You'll need JavaScript enabled and the latest version of the Flash player to view Circles Are Awesome.
If you're sure you have Flash Player, you can still try viewing Circles Are Awesome
(Text from Circles Are Awesome)
Circles Are Awesome
by Jeff Weir
http://windowseat.ca
Circles have a rather intersting property. Just like triangles, you only need three points to create one.
So how do three points "define" a circle? Well, let's start by drawing three points and calling them A, B and C.
Now that we have three points, let's draw two lines: one from A to B, and one from B to C.
Next, we'll find the midpoints of the line segments we just drew.
At each midpoint, draw a perpendicular line in both directions. We'll draw a point where the lines meet and call it D.
D is now the center of the circle. For proof, we'll draw a line from D to the points A, B and C.
These lines are all the same length. If we rotate them around point D, we'll find a circle has been created.
But will A, B and C always define a circle? Try moving the points around to find out.
You found the point where A, B and C don't define a circle.
When A, B and C make a perfectly straight line, the perpendicular lines will never intersect. This means the center of the circle doesn't exist.
So three points don't always define a circle.
Now that we know how to make a circle with three points, what happens when we use B, C and D to define E?
We get another circle. In fact, we can go on forever making circles from other circles. But that's for you to play with...