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National and Regional Contests
Belgium Contests
Flanders Math Olympiad
1996 Flanders Math Olympiad
1
Geometry (flanders '96)
Geometry (flanders '96)
Source:
August 9, 2004
geometry
trigonometry
Problem Statement
In triangle
Δ
A
D
C
\Delta ADC
Δ
A
D
C
we got
A
D
=
D
C
AD=DC
A
D
=
D
C
and
D
=
10
0
∘
D=100^\circ
D
=
10
0
∘
. In triangle
Δ
C
A
B
\Delta CAB
Δ
C
A
B
we got
C
A
=
A
B
CA=AB
C
A
=
A
B
and
A
=
2
0
∘
A=20^\circ
A
=
2
0
∘
. Prove that
A
B
=
B
C
+
C
D
AB=BC+CD
A
B
=
BC
+
C
D
.
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