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2018 Moldova Team Selection Test
7
Cute geometry
Cute geometry
Source: Moldova TST 2018
April 6, 2018
geometry
Problem Statement
Let the triangle
A
B
C
ABC
A
BC
with
m
(
∠
A
B
C
)
=
6
0
∘
m (\angle ABC)=60^{\circ}
m
(
∠
A
BC
)
=
6
0
∘
and
m
(
∠
B
A
C
)
=
4
0
∘
m (\angle BAC)=40^{\circ}
m
(
∠
B
A
C
)
=
4
0
∘
. Points
D
D
D
and
E
E
E
are on the sides
(
A
B
)
(AB)
(
A
B
)
and
(
A
C
)
(AC)
(
A
C
)
such that
m
(
∠
D
C
B
)
=
7
0
∘
m (\angle DCB )=70^{\circ}
m
(
∠
D
CB
)
=
7
0
∘
and
m
(
∠
E
B
C
)
=
4
0
∘
m (\angle EBC)=40^{\circ}
m
(
∠
EBC
)
=
4
0
∘
.
B
E
BE
BE
and
C
D
CD
C
D
intersect in
F
F
F
. Prove that
B
C
BC
BC
and
A
F
AF
A
F
are perpendicular.
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