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National and Regional Contests
Mexico Contests
Mexico National Olympiad
1989 Mexico National Olympiad
1
1
Part of
1989 Mexico National Olympiad
Problems
(1)
perpendicular medians in a triangle with given third side and area
Source: Mexican Mathematical Olympiad 1989 OMM P1
7/27/2018
In a triangle
A
B
C
ABC
A
BC
the area is
18
18
18
, the length
A
B
AB
A
B
is
5
5
5
, and the medians from
A
A
A
and
B
B
B
are orthogonal. Find the lengths of the sides
B
C
,
A
C
BC,AC
BC
,
A
C
.
geometry
Medians
area of a triangle
perpendicular