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CMIMC Problems
2021 CMIMC
12
12
Part of
2021 CMIMC
Problems
(1)
2021 Team P12
Source:
3/2/2021
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle, and let
l
l
l
be the line passing through its incenter and centroid. Assume that
B
B
B
and
C
C
C
lie on the same side of
l
l
l
, and that the distance from
B
B
B
to
l
l
l
is twice the distance from
C
C
C
to
l
l
l
. Suppose also that the length
B
A
BA
B
A
is twice that of
C
A
CA
C
A
. If
△
A
B
C
\triangle ABC
△
A
BC
has integer side lengths and is as small as possible, what is
A
B
2
+
B
C
2
+
C
A
2
AB^2+BC^2+CA^2
A
B
2
+
B
C
2
+
C
A
2
?Proposed by Thomas Lam
geometry