In any triangle ABC, the perpendicular bisectors of any two or three sides will meet in one point that is equidistant from all three points. Call this point D. You can draw a circle around center D with radius DB and it will intersect all of the points in the triangle. A figure is cyclic if there is a circle which can be drawn through all the points of the figure. Every triangle is cyclic, but every quadrilateral is not. The rule for polygons is that "if the perpendicular bisectors of all the sides meet at one point, then the polygon is cyclic.

In the third figure, triangle ABC is a right triangle. It is interesting to note that in a right triangle, the perpendicular bisectors meet on the midpoint of the hypotenuse (the longest side).

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