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Sharygin Geometry Olympiad
2023 Sharygin Geometry Olympiad
8.5
8.5
Part of
2023 Sharygin Geometry Olympiad
Problems
(1)
find BD if MO = a and OC = b
Source: Sharygin Finals 2023 8.5
8/2/2023
The median
C
M
CM
CM
and the altitude
A
H
AH
A
H
of an acute-angled triangle
A
B
C
ABC
A
BC
meet at point
O
O
O
. A point
D
D
D
lies outside the triangle in such a way that
A
O
C
D
AOCD
A
OC
D
is a parallelogram. Find the length of
B
D
BD
B
D
, if
M
O
=
a
MO= a
MO
=
a
,
O
C
=
b
OC = b
OC
=
b
.
geometry
Sharygin Geometry Olympiad
Sharygin 2023