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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2021 Sharygin Geometry Olympiad
16
16
Part of
2021 Sharygin Geometry Olympiad
Problems
(1)
Bisection in internally tangent circles
Source: XVII Sharygin Correspondence Round, P16
3/2/2021
Let circles
Ω
\Omega
Ω
and
ω
\omega
ω
touch internally at point
A
A
A
. A chord
B
C
BC
BC
of
Ω
\Omega
Ω
touches
ω
\omega
ω
at point
K
K
K
. Let
O
O
O
be the center of
ω
\omega
ω
. Prove that the circle
B
O
C
BOC
BOC
bisects segment
A
K
AK
A
K
.
circle
geometry