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National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2006.5
2006.5
Part of
Swiss NMO - geometry
Problems
(1)
concyclic wanted, 2 circles internally tangent
Source: Switzerland - Swiss MO 2006 p5
7/18/2020
A circle
k
1
k_1
k
1
lies within a second circle
k
2
k_2
k
2
and touches it at point
A
A
A
. A line through
A
A
A
intersects
k
1
k_1
k
1
again in
B
B
B
and
k
2
k_2
k
2
in
C
C
C
. The tangent to
k
1
k_1
k
1
through
B
B
B
intersects
k
2
k_2
k
2
at points
D
D
D
and
E
E
E
. The tangents at
k
1
k_1
k
1
passing through
C
C
C
intersects
k
1
k_1
k
1
in points
F
F
F
and
G
G
G
. Prove that
D
,
E
,
F
D, E, F
D
,
E
,
F
and
G
G
G
lie on a circle.
geometry
Concyclic
circles