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6
2017 G6: Angle Difference in Cyclic Quadrilateral
2017 G6: Angle Difference in Cyclic Quadrilateral
Source:
January 29, 2017
2017
geometry
cyclic quadrilateral
Problem Statement
Cyclic quadrilateral
A
B
C
D
ABCD
A
BC
D
satisfies
∠
A
B
D
=
7
0
∘
\angle ABD = 70^\circ
∠
A
B
D
=
7
0
∘
,
∠
A
D
B
=
5
0
∘
\angle ADB=50^\circ
∠
A
D
B
=
5
0
∘
, and
B
C
=
C
D
BC=CD
BC
=
C
D
. Suppose
A
B
AB
A
B
intersects
C
D
CD
C
D
at point
P
P
P
, while
A
D
AD
A
D
intersects
B
C
BC
BC
at point
Q
Q
Q
. Compute
∠
A
P
Q
−
∠
A
Q
P
\angle APQ-\angle AQP
∠
A
PQ
−
∠
A
QP
.
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