MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Stanford Mathematics Tournament
2014 Stanford Mathematics Tournament
4
4
Part of
2014 Stanford Mathematics Tournament
Problems
(1)
SMT RMT 2014 Geometry #4
Source:
10/28/2022
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
geometry