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2020 Stanford Mathematics Tournament
9
9
Part of
2020 Stanford Mathematics Tournament
Problems
(1)
SMT 2020 Geometry #9 right triangle
Source:
8/9/2023
Let
A
B
C
ABC
A
BC
be a right triangle with hypotenuse
A
C
AC
A
C
. Let
G
G
G
be the centroid of this triangle and suppose that we have
A
G
2
+
B
G
2
+
C
G
2
=
156
AG^2 + BG^2 + CG^2 = 156
A
G
2
+
B
G
2
+
C
G
2
=
156
. Find
A
C
2
AC^2
A
C
2
.
geometry