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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
8.1
8.1
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Reflections of circumcenter
Source: Sharygin Finals 2022 8.1
10/3/2022
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral with
∠
B
A
D
=
2
∠
B
C
D
\angle{BAD} = 2\angle{BCD}
∠
B
A
D
=
2∠
BC
D
and
A
B
=
A
D
AB = AD
A
B
=
A
D
. Let
P
P
P
be a point such that
A
B
C
P
ABCP
A
BCP
is a parallelogram. Prove that
C
P
=
D
P
CP = DP
CP
=
D
P
.
geometry
geometric transformation
reflection
circumcircle