# an interesting function on quadrilaterals

Before exploring this applet please study the Circumcenter-finder applet here. Here is function from the space of quadrilaterals to the space of quadrilaterals. Consider the four points [Yellow dots] which form the quadrilateral ABCD [green]. Circumscribe circles around ABC [center will be at E], around BCD [center will be at F], around CDA [center will be at G] and around DAB [center will be at G]. The centers form the quadrilateral EFGH [blue]. If you carry out the same procedure on the blue quadrilateral you get the orange quadrilateral. Drag the Yellow dots - ﻿ ﻿ ﻿ ﻿ ﻿conjectures? ﻿ ﻿ ﻿ ﻿ ﻿proofs? ﻿ ﻿ ﻿ ﻿ ﻿extensions? What questions could / would you put to your students based on this applet?
Now suppose we change the function so that it now reads - Consider the four points [Yellow dots] which form the quadrilateral ABCD [green]. Inscribe circles in ABC [center will be at E], in BCD [center will be at F], in CDA [center will be at G] and in DAB [center will be at G]. The centers form a new quadrilateral EFGH. If you carry out the same procedure on EFGH what will you get?