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Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
22
Classic Geo Overload
Classic Geo Overload
Source: Sharygin 2022 P22
March 4, 2022
geometry
Problem Statement
Chords
A
1
A
2
,
A
3
A
4
,
A
5
A
6
A_1A_2, A_3A_4, A_5A_6
A
1
A
2
,
A
3
A
4
,
A
5
A
6
of a circle
Ω
\Omega
Ω
concur at point
O
O
O
. Let
B
i
B_i
B
i
be the second common point of
Ω
\Omega
Ω
and the circle with diameter
O
A
i
OA_i
O
A
i
. Prove that chords
B
1
B
2
,
B
3
B
4
,
B
5
B
6
B_1B_2, B_3B_4, B_5B_6
B
1
B
2
,
B
3
B
4
,
B
5
B
6
concur.
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