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National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2010.89.4
2010.89.4
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
angle chasing, OD = BD = 1/3 BC (Kyiv City Olympiad 2010 8.4 9.6)
Source:
7/2/2020
Point
O
O
O
is the center of the circumcircle of the acute triangle
A
B
C
ABC
A
BC
. The line
A
O
AO
A
O
intersects the side
B
C
BC
BC
at point
D
D
D
so that
O
D
=
B
D
=
1
/
3
B
C
OD = BD = 1/3 BC
O
D
=
B
D
=
1/3
BC
. Find the angles of the triangle
A
B
C
ABC
A
BC
. Justify the answer.
geometry
angles
Circumcenter