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Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
1976 Poland - Second Round
4
4
Part of
1976 Poland - Second Round
Problems
(1)
concyclic points
Source: Polish MO Second Round 1976 p4
9/8/2024
Inside the circle
S
S
S
there is a circle
T
T
T
and circles
K
1
,
K
2
,
…
,
K
n
K_1, K_2, \ldots, K_n
K
1
,
K
2
,
…
,
K
n
tangent externally to
T
T
T
and internally to
S
S
S
, and the circle
K
1
K_1
K
1
is tangent to
K
2
K_2
K
2
,
K
2
K_2
K
2
tangent to
K
3
K_3
K
3
etc. Prove that the points of tangency of the circles
K
1
K_1
K
1
with
K
2
K_2
K
2
,
K
2
K_2
K
2
with
K
3
K_3
K
3
etc. lie on the circle.
geometry
Concyclic