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National and Regional Contests
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All-Russian Olympiad
1972 All Soviet Union Mathematical Olympiad
165
165
Part of
1972 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 165 All Soviet Union MO 1972 perpendiculars inside a convex ABCD
Source:
7/3/2019
Let
O
O
O
be the intersection point of the diagonals of the convex quadrangle
A
B
C
D
ABCD
A
BC
D
. Prove that the line drawn through the points of intersection of the medians of triangles
A
O
B
AOB
A
OB
and
C
O
D
COD
CO
D
is orthogonal to the line drawn through the points of intersection of the heights of triangles
B
O
C
BOC
BOC
and
A
O
D
AOD
A
O
D
.
geometry
perpendicular