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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1998 All-Russian Olympiad Regional Round
11.2
11.2
Part of
1998 All-Russian Olympiad Regional Round
Problems
(1)
DE _|_ OC, interssecting circles
Source: - All-Russian MO 1998 Regional (R4) 11.2
9/17/2024
Circle
S
S
S
with center
O
O
O
and circle
S
′
S'
S
′
intersect at points
A
A
A
and
B
B
B
. Point
C
C
C
is taken on the arc of a circle
S
S
S
lying inside
S
′
S'
S
′
. Denote the intersection points of
A
C
AC
A
C
and
B
C
BC
BC
with
S
′
S'
S
′
, other than
A
A
A
and
B
B
B
, as
E
E
E
and
D
D
D
, respectively. Prove that lines
D
E
DE
D
E
and
O
C
OC
OC
are perpendicular.
perpendicular
geometry