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National and Regional Contests
Greece Contests
Greece JBMO TST
2015 Greece JBMO TST
2
2
Part of
2015 Greece JBMO TST
Problems
(1)
two circumcenters and one orthocenter, vertices of parallelogram
Source: Greece JBMO TST 2015 p2
4/29/2019
Let
A
B
C
ABC
A
BC
be an acute triangle inscribed in a circle of center
O
O
O
. If the altitudes
B
D
,
C
E
BD,CE
B
D
,
CE
intersect at
H
H
H
and the circumcenter of
△
B
H
C
\triangle BHC
△
B
H
C
is
O
1
O_1
O
1
, prove that
A
H
O
1
O
AHO_1O
A
H
O
1
O
is a parallelogram.
geometry
circumcircle
parallelogram
orthocenter