There are two very nice problems. For those curious I posted a dynamic illustration to the first of them athttp://www.cut-the-knot.org/Curriculum/Geometry/MarkowskyParabola.shtmland a related problem at http://www.cut-the-knot.org/Curriculum/Geometry/Markowsky2.shtml
http://www.cut-the-knot.org/Curriculum/Geometry/MarkowskyParabola.shtml
and a related problem at
http://www.cut-the-knot.org/Curriculum/Geometry/Markowsky2.shtml