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National and Regional Contests
Latvia Contests
Latvia BW TST
2019 Latvia Baltic Way TST
9
9
Part of
2019 Latvia Baltic Way TST
Problems
(1)
Standard angle chase
Source: Latvian TST for Baltic Way 2019 Problem 9
11/30/2020
Let
A
B
C
D
ABCD
A
BC
D
be a rhombus with the condition
∠
A
B
C
>
9
0
o
\angle ABC > 90^o
∠
A
BC
>
9
0
o
. The circle
Γ
B
\Gamma_B
Γ
B
with center at
B
B
B
goes through
C
C
C
, and the circle
Γ
C
\Gamma_C
Γ
C
with center at
C
C
C
goes through
B
B
B
. Denote by
E
E
E
one of the intersection points of
Γ
B
\Gamma_B
Γ
B
and
Γ
C
\Gamma_C
Γ
C
. The line
E
D
ED
E
D
intersects intersects
Γ
B
\Gamma_B
Γ
B
again at
F
F
F
. Find the value of
∠
A
F
B
\angle AFB
∠
A
FB
.
geometry
rhombus