1992 OIM Problems/Problem 3
Problem
In an equilateral triangle whose side has length 2, the circle
is inscribed.
a. Show that for every point of
, the sum of the squares of its distances to the vertices
,
and
is 5.
b. Show that for every point in
it is possible to construct a triangle whose sides have the lengths of the segments
,
and
, and that its area is:
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.