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National and Regional Contests
Germany Contests
German National Olympiad
1997 German National Olympiad
3
angle chasing inside a quadrilateral
angle chasing inside a quadrilateral
Source: Germany 1997 p3
February 22, 2020
Angle Chasing
angles
geometry
Problem Statement
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
we are given that
∠
C
B
D
=
1
0
o
\angle CBD = 10^o
∠
CB
D
=
1
0
o
,
∠
C
A
D
=
2
0
o
\angle CAD = 20^o
∠
C
A
D
=
2
0
o
,
∠
A
B
D
=
4
0
o
\angle ABD = 40^o
∠
A
B
D
=
4
0
o
,
∠
B
A
C
=
5
0
o
\angle BAC = 50^o
∠
B
A
C
=
5
0
o
. Determine the angles
∠
B
C
D
\angle BCD
∠
BC
D
and
∠
A
D
C
\angle ADC
∠
A
D
C
.
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