Given a triangle ABC, points D,E,F are defined to be proportion t along the sides AB, BC, CA respectively.
Point G is at the intersection of AE and BF.
Point H is at the intersection of BF and CD.
Point I is at the intersection of CD and AE.
Using Geometry Expressions (or otherwise) show that the loci of G,H and I as t varies are portions of ellipses.
Show further that they are portions of the same (translated) ellipse.
An app illustrating this property is
here.
Under what circumstances is the ellipse a circle?