Cyclic Quadrangle
Let 
, 
, 
, and 
be four Points on a Circle, and 
, 
, 
, 
theOrthocenters of Triangles 
, etc. If, from the eightPoints, four with different subscripts are chosen such that three are from one set and the fourth from theother, these Points form an Orthocentric System. There are eight such systems, which areanalogous to the six sets of Orthocentric Systems obtained using the feet of theAngle Bisectors, Orthocenter, and Vertices of a generic Triangle.
On the other hand, if all the Points are chosen from one set, or two from each set, with all differentsubscripts, the four Points lie on a Circle. There are four pairs of suchCircles, and eight Points lie by fours on eight equal Circles.
The Simson Line of with regard to Triangle 
is the same as that of with regard tothe Triangle 
.
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 251-253, 1929.
- Double Sixes
- Double Sum
- Doublet Function
- Doubly Even Number
- Doubly Magic Square
- Dougall-Ramanujan Identity
- Dougall's Theorem
- Doughnut
- Douglas-Neumann Theorem
- Dovetailing Problem
- Dowker Notation
- Down Arrow Notation
- Dozen
- Dragon Curve
- Dragon Fractal
- Draughts
- Drinfeld's Symmetric Space
- Droz-Farny Circles
- Drum
- D-Statistic
- D-Triangle
- Dual Basis
- Dual Bivector
- Dual Graph
- Duality Principle