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Kvant 2019
M2554
M2554
Part of
Kvant 2019
Problems
(1)
Easy geo with tangent circles
Source: Kvant Magazine No. 4 M2554
3/14/2023
Two externally tangent circles
Ω
1
\Omega_1
Ω
1
and
Ω
2
\Omega_2
Ω
2
are internally tangent to the circle
Ω
\Omega
Ω
at
A
A
A
and
B
B
B
, respectively. If the line
A
B
AB
A
B
intersects
Ω
1
\Omega_1
Ω
1
again at
D
D
D
and
C
∈
Ω
1
∩
Ω
2
C\in\Omega_1\cap\Omega_2
C
∈
Ω
1
∩
Ω
2
, show that
∠
B
C
D
=
9
0
∘
\angle BCD=90^\circ
∠
BC
D
=
9
0
∘
.Proposed by V. Rastorguev
geometry
Kvant