Let I, J, K, and L be the incenter and the three excenters of triangle ABC.

What is the center of gravity of these four points?

(In reply to re: ???? by Charlie)

As the problem is given as a level 3 puzzle, I am guessing that we are trying to find the "center of gravity" of only four points, zero dimensional planar laminae.  Being zero-dimensional planar lamina, each point is a center of zero mass.  Applying the equation to find the barycenter between any two of these points results in an attempt to divide by zero.  Therefore the answer to the question "What is the center of gravity of these four points?" is....
"indeterminate",
or, in Bhaskara Achârya's interpretation of the value of division by zero,...
"every-point".

Edited on February 7, 2008, 12:26 pm

Posted by Dej Mar on 2008-02-07 12:10:47