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Junior Balkan MO
2007 Junior Balkan MO
2
2
Part of
2007 Junior Balkan MO
Problems
(1)
balkan "slicing" problem
Source: JBMO 2007, Bulgaria, problem 2
6/28/2007
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral with
∠
D
A
C
=
∠
B
D
C
=
3
6
∘
\angle{DAC}= \angle{BDC}= 36^\circ
∠
D
A
C
=
∠
B
D
C
=
3
6
∘
,
∠
C
B
D
=
1
8
∘
\angle{CBD}= 18^\circ
∠
CB
D
=
1
8
∘
and
∠
B
A
C
=
7
2
∘
\angle{BAC}= 72^\circ
∠
B
A
C
=
7
2
∘
. The diagonals and intersect at point
P
P
P
. Determine the measure of
∠
A
P
D
\angle{APD}
∠
A
P
D
.
trigonometry
geometry
incenter
function
circumcircle
cyclic quadrilateral
angle bisector