MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2020 Latvia Baltic Way TST
12
12
Part of
2020 Latvia Baltic Way TST
Problems
(1)
Rhombus and 2 circles
Source: Latvian TST for Baltic Way 2020 P12
10/18/2020
There are rhombus
A
B
C
D
ABCD
A
BC
D
and circle
Γ
B
\Gamma_B
Γ
B
, which is centred at
B
B
B
and has radius
B
C
BC
BC
, and circle
Γ
C
\Gamma_C
Γ
C
, which is centred at
C
C
C
and has radius
B
C
BC
BC
. Circles
Γ
B
\Gamma_B
Γ
B
and
Γ
C
\Gamma_C
Γ
C
intersect at point
E
E
E
. The line
E
D
ED
E
D
intersects
Γ
B
\Gamma_B
Γ
B
at point
F
F
F
. Find all possible values of
∠
A
F
B
\angle AFB
∠
A
FB
.
geometry
rhombus