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4
SMT RMT 2014 Geometry #4
SMT RMT 2014 Geometry #4
Source:
October 28, 2022
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle such that
A
B
=
3
AB = 3
A
B
=
3
,
B
C
=
4
BC = 4
BC
=
4
, and
A
C
=
5
AC = 5
A
C
=
5
. Let
X
X
X
be a point in the triangle. Compute the minimal possible value of
A
X
2
+
B
X
2
+
C
X
2
AX^2 + BX^2 + CX^2
A
X
2
+
B
X
2
+
C
X
2
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