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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2000 All-Russian Olympiad Regional Round
8.7
8.7
Part of
2000 All-Russian Olympiad Regional Round
Problems
(1)
KO _|_ AC, symmetric, incenter - All-Russian MO 2000 Regional (R4) 8.7
Source:
9/25/2024
Angle bisectors
A
D
AD
A
D
and
C
E
CE
CE
of triangle
A
B
C
ABC
A
BC
intersect at point
O
O
O
. A line symmetrical to
A
B
AB
A
B
with respect to
C
E
CE
CE
intersects the line symmetric
B
C
BC
BC
with respect to
A
D
AD
A
D
, at point
K
K
K
. Prove that
K
O
⊥
A
C
KO \perp AC
K
O
⊥
A
C
.
geometry
incenter