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Poland - Second Round
2022 Poland - Second Round
4
4
Part of
2022 Poland - Second Round
Problems
(1)
Polish MO 2022 P4
Source: Polish MO 2022 P4
2/12/2022
Given quadrilateral
A
B
C
D
ABCD
A
BC
D
inscribed into a circle with diagonal
A
C
AC
A
C
as diameter. Let
E
E
E
be a point on segment
B
C
BC
BC
s.t.
∢
D
A
C
=
∢
E
A
B
\sphericalangle DAC=\sphericalangle EAB
∢
D
A
C
=
∢
E
A
B
. Point
M
M
M
is midpoint of
C
E
CE
CE
. Prove that
B
M
=
D
M
BM=DM
BM
=
D
M
.
geometry