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1969 IMO Shortlist
5
5
Part of
1969 IMO Shortlist
Problems
(1)
Prove all conics are hyperbolas and find locus of centers.
Source:
9/29/2010
(
B
E
L
5
)
(BEL 5)
(
BE
L
5
)
Let
G
G
G
be the centroid of the triangle
O
A
B
.
OAB.
O
A
B
.
(
a
)
(a)
(
a
)
Prove that all conics passing through the points
O
,
A
,
B
,
G
O,A,B,G
O
,
A
,
B
,
G
are hyperbolas.
(
b
)
(b)
(
b
)
Find the locus of the centers of these hyperbolas.
conics
hyperbola
geometry
circumcircle
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