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International Contests
IMO Longlists
1971 IMO Longlists
48
48
Part of
1971 IMO Longlists
Problems
(1)
O in ABCD making angles of 30 and 45 degrees [ILL 1971]
Source:
1/1/2011
The diagonals of a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
intersect at a point
O
O
O
. Find all angles of this quadrilateral if
∡
O
B
A
=
3
0
∘
,
∡
O
C
B
=
4
5
∘
,
∡
O
D
C
=
4
5
∘
\measuredangle OBA=30^{\circ},\measuredangle OCB=45^{\circ},\measuredangle ODC=45^{\circ}
∡
OB
A
=
3
0
∘
,
∡
OCB
=
4
5
∘
,
∡
O
D
C
=
4
5
∘
, and
∡
O
A
D
=
3
0
∘
\measuredangle OAD=30^{\circ}
∡
O
A
D
=
3
0
∘
.
geometry proposed
geometry