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Russia Contests
All-Russian Olympiad Regional Round
1995 All-Russian Olympiad Regional Round
9.6
9.6
Part of
1995 All-Russian Olympiad Regional Round
Problems
(1)
CD = CB = CE, 2 circles All-Russian MO 1995 Regional (R4) 9.6
Source:
8/26/2024
Circles
S
1
S_1
S
1
and
S
2
S_2
S
2
with centers
O
1
O_1
O
1
and
O
2
O_2
O
2
respectively intersect at
A
A
A
and
B
B
B
. The circle passing through
O
1
O_1
O
1
,
O
2
O_2
O
2
, and
A
A
A
intersects
S
1
S_1
S
1
,
S
2
S_2
S
2
and line
A
B
AB
A
B
again at
D
D
D
,
E
E
E
, and
C
C
C
, respectively. Show that
C
D
=
C
B
=
C
E
CD = CB = CE
C
D
=
CB
=
CE
.
geometry
circles
equal segments