MathDB
Problems
Contests
National and Regional Contests
Croatia Contests
Croatia National Olympiad
2004 Croatia National Olympiad
Problem 2
orthogonal medians (Croatian MO 2004 1st Grade P2)
orthogonal medians (Croatian MO 2004 1st Grade P2)
Source:
April 8, 2021
geometry
Problem Statement
Prove that the medians from the vertices
A
A
A
and
B
B
B
of a triangle
A
B
C
ABC
A
BC
are orthogonal if and only if
B
C
2
+
A
C
2
=
5
A
B
2
BC^2+AC^2=5AB^2
B
C
2
+
A
C
2
=
5
A
B
2
.
Back to Problems
View on AoPS