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3
4(m_a^2+m_b^2+m_c^2)=3(a^2+b^2+c^2)
4(m_a^2+m_b^2+m_c^2)=3(a^2+b^2+c^2)
Source: Kosovo IMO TST 2012 problem 3
April 22, 2012
geometry
parallelogram
geometry proposed
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are the sides of a triangle and
m
a
,
m
b
,
m
c
m_a , m_b, m_c
m
a
,
m
b
,
m
c
are the medians prove that
4
(
m
a
2
+
m
b
2
+
m
c
2
)
=
3
(
a
2
+
b
2
+
c
2
)
4(m_a^2+m_b^2+m_c^2)=3(a^2+b^2+c^2)
4
(
m
a
2
+
m
b
2
+
m
c
2
)
=
3
(
a
2
+
b
2
+
c
2
)
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