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National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Seniors Round2 2010+ geometry
2018.10.3.1
2018.10.3.1
Part of
Kyiv City MO Seniors Round2 2010+ geometry
Problems
(1)
perpendicular wanted circumcircle related (2018 Kyiv City MO Round2 10.3.1)
Source:
9/14/2020
The point
O
O
O
is the center of the circumcircle of the acute triangle
A
B
C
ABC
A
BC
. The line
A
C
AC
A
C
intersects the circumscribed circle
Δ
A
B
O
\Delta ABO
Δ
A
BO
for second time at the point
X
X
X
. Prove that
X
O
⊥
B
C
XO \bot BC
XO
⊥
BC
.
geometry
circumcircle
perpendicular