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Belarus Team Selection Test
2024 Belarus Team Selection Test
4.3
4.3
Part of
2024 Belarus Team Selection Test
Problems
(1)
Easy looking geometry not very easy to solve
Source: Belarus TST 2024
7/17/2024
An isosceles triangle
A
B
C
ABC
A
BC
is given(
A
B
=
B
C
AB=BC
A
B
=
BC
). Point
D
D
D
lies inside of it such that
∠
A
D
C
=
150
\angle ADC=150
∠
A
D
C
=
150
,
E
E
E
lies on
C
D
CD
C
D
such that
A
E
=
A
B
AE=AB
A
E
=
A
B
. It turned out that
∠
E
B
C
+
∠
B
A
E
=
60
\angle EBC+\angle BAE=60
∠
EBC
+
∠
B
A
E
=
60
. Prove that
∠
B
D
C
+
∠
C
A
E
=
90
\angle BDC+\angle CAE=90
∠
B
D
C
+
∠
C
A
E
=
90
D. Vasilyev
geometry