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All-Russian Olympiad Regional Round
2001 All-Russian Olympiad Regional Round
11.3
11.3
Part of
2001 All-Russian Olympiad Regional Round
Problems
(1)
common tangent of 3 circles - All-Russian MO 2001 Regional (R4) 11.3
Source:
9/26/2024
Let
A
D
AD
A
D
be the angle bisector of triangle
A
B
C
ABC
A
BC
, and let the line
ℓ
\ell
ℓ
touch circumcircles of triangles
A
D
B
ADB
A
D
B
and
A
D
C
ADC
A
D
C
at points
M
M
M
and
N
N
N
accordingly. Prove that the circle passing through the midpoints of the segments
B
D
BD
B
D
,
D
C
DC
D
C
and
M
N
MN
MN
is tangent to the line
ℓ
\ell
ℓ
.
geometry
tangent