# an interesting function on quadrilaterals

- Author:
- Judah L Schwartz

- Topic:
- Geometry, Quadrilaterals

Before exploring this applet please study the

*applet***Circumcenter-finder***. Here is function from the space of quadrilaterals to the space of quadrilaterals. Consider the four points [***here****dots] which form the quadrilateral ABCD [***Yellow**]. 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 [***green***]. If you carry out the same procedure on the blue quadrilateral you get the***blue***quadrilateral. Drag the***orange***dots - conjectures? proofs? extensions?***Yellow****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 [

**dots] which form the quadrilateral ABCD [***Yellow**].***green***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?***Inscribe**