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South Africa National Olympiad
2002 South africa National Olympiad
1
1
Part of
2002 South africa National Olympiad
Problems
(1)
Easy geometry
Source: South Africa 2002
10/13/2005
Given a quadrilateral
A
B
C
D
ABCD
A
BC
D
such that
A
B
2
+
C
D
2
=
A
D
2
+
B
C
2
AB^2 + CD^2 = AD^2 + BC^2
A
B
2
+
C
D
2
=
A
D
2
+
B
C
2
, prove that
A
C
⊥
B
D
AC \perp BD
A
C
⊥
B
D
.
geometry
trigonometry
vector
analytic geometry
trig identities
Law of Cosines