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2001 JBMO ShortLists
9
Equal angles in a convex quadrilateral
Equal angles in a convex quadrilateral
Source: JBMO Shortlist 2001
October 30, 2010
geometry proposed
geometry
Problem Statement
Consider a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
with
A
B
=
C
D
AB=CD
A
B
=
C
D
and
∠
B
A
C
=
3
0
∘
\angle BAC=30^{\circ}
∠
B
A
C
=
3
0
∘
. If
∠
A
D
C
=
15
0
∘
\angle ADC=150^{\circ}
∠
A
D
C
=
15
0
∘
, prove that
∠
B
C
A
=
∠
A
C
D
\angle BCA= \angle ACD
∠
BC
A
=
∠
A
C
D
.
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