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Triangles Inscribed in a Circle

Move one or more of the points C, D, E, until you have a right triangle (one of the angles is 90 degrees.) What do you notice about the side opposite the right angle?
The side opposite the right angle goes through the center of the circle. That is, it's a diameter of the circle. Why is this so? Try to prove it. You can also look up a proof. Technical term: a circle is inscribed in a circle if its vertices are all on the circle.