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2021 Latvia TST
1.3
1.3
Part of
2021 Latvia TST
Problems
(1)
Isosceles triangle and strange point and angle
Source: Latvian TST 2021 Day 1 P3
3/12/2021
Given isosceles
△
A
B
C
\triangle ABC
△
A
BC
with
A
B
=
A
C
AB = AC
A
B
=
A
C
and
∠
B
A
C
=
2
2
∘
\angle BAC = 22^{\circ}
∠
B
A
C
=
2
2
∘
. On the side
B
C
BC
BC
point
D
D
D
is chosen such that
B
D
=
2
C
D
BD = 2CD
B
D
=
2
C
D
. The foots of perpendiculars from
B
B
B
to lines
A
D
AD
A
D
and
A
C
AC
A
C
are points
E
E
E
,
F
F
F
respectively. Find with the proof value of the angle
∠
C
E
F
\angle CEF
∠
CEF
.
geometry