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Kvant 2019
M2547
M2547
Part of
Kvant 2019
Problems
(1)
Parallelism is Sangaku configuration
Source: Kvant Magazine No. 2 2019 M2547
3/14/2023
The circles
ω
1
\omega_1
ω
1
and
ω
2
\omega_2
ω
2
centered at
O
1
O_1
O
1
and
O
2
O_2
O
2
are externally tangent at the point
T
T
T
. The circle
ω
3
\omega_3
ω
3
centered at
O
3
O_3
O
3
is tangent to the line
A
B
AB
A
B
(the external common tangent of
ω
1
\omega_1
ω
1
and
ω
2
\omega_2
ω
2
) at
D
D
D
and externally tangent to
ω
1
\omega_1
ω
1
and to
ω
2
\omega_2
ω
2
. The line
T
D
TD
T
D
intersects again at
ω
1
\omega_1
ω
1
. Prove that
O
1
C
∥
A
B
O_1 C \parallel AB
O
1
C
∥
A
B
. [I]Proposed by V. Rastorguev[/I]
geometry
Kvant