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Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
2000 Canada National Olympiad
4
4
Part of
2000 Canada National Olympiad
Problems
(1)
Prove quadrilateral is kite
Source: Canada 2000
3/4/2006
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral with
∠
C
B
D
=
2
∠
A
D
B
\angle CBD = 2 \angle ADB
∠
CB
D
=
2∠
A
D
B
,
∠
A
B
D
=
2
∠
C
D
B
\angle ABD = 2 \angle CDB
∠
A
B
D
=
2∠
C
D
B
and
A
B
=
C
B
AB = CB
A
B
=
CB
. Prove that
A
D
=
C
D
AD = CD
A
D
=
C
D
.
geometry
geometric transformation
reflection
circumcircle
trigonometry
perpendicular bisector
geometry unsolved