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Poland Contests
Polish Junior Math Olympiad
2018 Polish Junior Math Olympiad
2018 Polish Junior MO First Round
4
4
Part of
2018 Polish Junior MO First Round
Problems
(1)
Equality of angles in trapezoid
Source: XIII Polish Junior MO 2018 First Round - Problem 4
4/24/2018
Let
A
B
C
D
ABCD
A
BC
D
be a trapezoid with bases
A
B
AB
A
B
and
C
D
CD
C
D
. Bisectors of
A
D
AD
A
D
and
B
C
BC
BC
intersect line segments
B
C
BC
BC
and
A
D
AD
A
D
respectively in points
P
P
P
and
Q
Q
Q
. Show that
∠
A
P
D
=
∠
B
Q
C
\angle APD = \angle BQC
∠
A
P
D
=
∠
BQC
.
geometry
trapezoid
bisector
Poland