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International Contests
Baltic Way
2022 Baltic Way
13
13
Part of
2022 Baltic Way
Problems
(1)
Right angle at the midpoint of EF
Source: Baltic Way 2022/13
11/12/2022
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral with
A
B
<
B
C
AB < BC
A
B
<
BC
and
A
D
<
D
C
AD < DC
A
D
<
D
C
. Let
E
E
E
and
F
F
F
be points on the sides
B
C
BC
BC
and
C
D
CD
C
D
, respectively, such that
A
B
=
B
E
AB = BE
A
B
=
BE
and
A
D
=
D
F
AD = DF
A
D
=
D
F
. Let further M denote the midpoint of the segment
E
F
EF
EF
. Prove that
∠
B
M
D
=
9
0
o
\angle BMD = 90^o
∠
BM
D
=
9
0
o
.
geometry