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Germany Team Selection Test
2017 Germany Team Selection Test
2
2
Part of
2017 Germany Team Selection Test
Problems
(1)
Convex Quadrilateral with Bisector Diagonal
Source: Germany TST 2017
4/11/2020
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
,
B
D
BD
B
D
is the angle bisector of
∠
A
B
C
\angle{ABC}
∠
A
BC
. The circumcircle of
A
B
C
ABC
A
BC
intersects
C
D
,
A
D
CD,AD
C
D
,
A
D
in
P
,
Q
P,Q
P
,
Q
respectively and the line through
D
D
D
parallel to
A
C
AC
A
C
cuts
A
B
,
A
C
AB,AC
A
B
,
A
C
in
R
,
S
R,S
R
,
S
respectively. Prove that point
P
,
Q
,
R
,
S
P,Q,R,S
P
,
Q
,
R
,
S
lie on a circle.
geometry