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South Africa Contests
South Africa National Olympiad
2010 South africa National Olympiad
2
2
Part of
2010 South africa National Olympiad
Problems
(1)
Sum of squares of lengths in a triangle
Source: South African MO 2010 Q2
5/26/2012
Consider a triangle
A
B
C
ABC
A
BC
with
B
C
=
3
BC = 3
BC
=
3
. Choose a point
D
D
D
on
B
C
BC
BC
such that
B
D
=
2
BD = 2
B
D
=
2
. Find the value of
A
B
2
+
2
A
C
2
ā
3
A
D
2
.
AB^2 + 2AC^2 - 3AD^2.
A
B
2
+
2
A
C
2
ā
3
A
D
2
.
trigonometry
geometry unsolved
geometry