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Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2018.9.51
2018.9.51
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
angle wanted, circle, midpoint, square related(2018 Kyiv City MO 9.5.1 )
Source:
9/12/2020
Given a circle
Γ
\Gamma
Γ
with center at point
O
O
O
and diameter
A
B
AB
A
B
.
O
B
D
E
OBDE
OB
D
E
is square,
F
F
F
is the second intersection point of the line
A
D
AD
A
D
and the circle
Γ
\Gamma
Γ
,
C
C
C
is the midpoint of the segment
A
F
AF
A
F
. Find the value of the angle
O
C
B
OCB
OCB
.
geometry
square
angles