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Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
8
8
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Locus of orthocentre of PQR is the diameter || to AC.
Source: Sharygin CR P8(Grades 8-9)
3/4/2022
Points
P
,
Q
,
R
P,Q,R
P
,
Q
,
R
lie on the sides
A
B
,
B
C
,
C
A
AB,BC,CA
A
B
,
BC
,
C
A
of triangle
A
B
C
ABC
A
BC
in such a way that
A
P
=
P
R
,
C
Q
=
Q
R
AP=PR, CQ=QR
A
P
=
PR
,
CQ
=
QR
. Let
H
H
H
be the orthocenter of triangle
P
Q
R
PQR
PQR
, and
O
O
O
be the circumcenter of triangle
A
B
C
ABC
A
BC
. Prove that
O
H
∣
∣
A
C
OH||AC
O
H
∣∣
A
C
.
Sharygin Geometry Olympiad
Sharygin 2022
geometry