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Bulgarian Spring Mathematical Competition
2024 Bulgarian Spring Mathematical Competition
12.2
12.2
Part of
2024 Bulgarian Spring Mathematical Competition
Problems
(1)
Iff angle conditions geometry
Source: Bulgarian Spring Tournament 2024 12.2
3/31/2024
Given is a triangle
A
B
C
ABC
A
BC
and two points
D
∈
A
C
,
E
∈
B
D
D \in AC, E \in BD
D
∈
A
C
,
E
∈
B
D
such that
∠
D
A
E
=
∠
A
E
D
=
∠
A
B
C
\angle DAE=\angle AED=\angle ABC
∠
D
A
E
=
∠
A
E
D
=
∠
A
BC
. Show that
B
E
=
2
C
D
BE=2CD
BE
=
2
C
D
iff
∠
A
C
B
=
9
0
∘
\angle ACB=90^{\circ}
∠
A
CB
=
9
0
∘
.
geometry