Let
be the incenter of a triangle and , , and be the intersections of the segments , , with the incircle. Also let
the centroid
lie inside the incircle and , , and be the intersections of the segments , , with the incircle. Then the perimeter of is less than or equal to that of , as proposed by Garfunkel (1981, 1982) and proved by
Nyugen and Dergiades (2004).
Garfunkel, J. "Problem 648." Crux Math.7, 178, 1981.Garfunkel, J. "Solution to Problem 648." Crux
Math.8, 180-182, 1982.Nyugen, M. H. and Dergiades,
N. "Garfunkel's Inequality." Forum Geom.4, 153-156, 2004.
http://forumgeom.fau.edu/FG2004volume4/FG200419index.html.
be the incenter of a triangle 
and 
, 
, and 
be the intersections of the segments 
, 
, 
with the incircle. Also let
the centroid 
lie inside the incircle and 
, 
, and 
be the intersections of the segments 
, 
, 
with the incircle. Then the perimeter of 
is less than or equal to that of 
, as proposed by Garfunkel (1981, 1982) and proved by
Nyugen and Dergiades (2004).
