Drag the large BLACK dots {A, B, C, D} to form a quadrilateral you are interested in.[br][br]This environment constructs a function, [call it [size=100][i][b]Q[/b][/i][/size]], from the space of quadrilaterals[br]to the space of quadrilaterals as follows - [br][br]--circumscribes a circle around points A,B,C with center at E[br][br]--circumscribes a circle around points B,C,D with center at F[br][br]--circumscribes a circle around points C,D,A with center at G[br][br]--circumscribes a circle around points D,A,B with center at H[br][br]and then constructs the quadrilateral EFGH (in GREEN)[br][br][i][b]Explore this function - what is the domain of Q ? the range of Q ?[br][/b][/i][br][i][b]Conjectures ?[br][br]Proofs ?[br][br]Extensions ?[/b][/i][br][br][color=#ff0000][b][i]Challenge - How cyclic is my quadrilateral ? [/i][br][br][i]Given a collection of n-sided polygons - some cyclic, others not - can you devise a measure of "cyclicity" - that is, a way of ordering them from "least cyclic" to cyclic ? [/i][/b][/color]

[color=#ff0000][b].[/b][/color]