1992 OIM Problems/Problem 3

Problem

In an equilateral triangle $ABC$ whose side has length 2, the circle $G$ is inscribed.

a. Show that for every point $P$ of $G$ , the sum of the squares of its distances to the vertices $A$ , $B$ and $C$ is 5.

b. Show that for every point $P$ in $G$ it is possible to construct a triangle whose sides have the lengths of the segments $AP$ , $BP$ and $CP$ , and that its area is:

$\frac{\sqrt{3}}{4}$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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1992 OIM Problems/Problem 3

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