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Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2012.8.3
2012.8.3
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
equal angles wanted, intersecting circles (2012 Kyiv City MO 8.3)
Source:
8/1/2020
On the circle
γ
\gamma
γ
the points
A
A
A
and
B
B
B
are selected. The circle
ω
\omega
ω
touches the segment
A
B
AB
A
B
at the point
K
K
K
and intersects the circle
γ
\gamma
γ
at the points
M
M
M
and
N
N
N
. The points lie on the circle
γ
\gamma
γ
in the following order:
A
,
M
,
N
,
B
A, \, \, M, \, \, N, \, \, B
A
,
M
,
N
,
B
. Prove that
∠
A
M
K
=
∠
K
N
B
\angle AMK = \angle KNB
∠
A
M
K
=
∠
K
NB
.(Yuri Biletsky)
geometry