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Baltic Way
1993 Baltic Way
19
19
Part of
1993 Baltic Way
Problems
(1)
Baltic way 93
Source: Easy
8/25/2007
A convex quadrangle
A
B
C
D
ABCD
A
BC
D
is inscribed in a circle with center
O
O
O
. The angles
A
O
B
,
B
O
C
,
C
O
D
AOB, BOC, COD
A
OB
,
BOC
,
CO
D
and
D
O
A
DOA
D
O
A
, taken in some order, are of the same size as the angles of the quadrangle
A
B
C
D
ABCD
A
BC
D
. Prove that
A
B
C
D
ABCD
A
BC
D
is a square
geometry
rectangle
rhombus
geometry unsolved