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Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2018 India PRMO
10
10
Part of
2018 India PRMO
Problems
(1)
2018 preRMO p10, (BC^2 + CA^2 + AB^2)/100, perp. medians
Source:
8/8/2019
In a triangle
A
B
C
ABC
A
BC
, the median from
B
B
B
to
C
A
CA
C
A
is perpendicular to the median from
C
C
C
to
A
B
AB
A
B
. If the median from
A
A
A
to
B
C
BC
BC
is
30
30
30
, determine
B
C
2
+
C
A
2
+
A
B
2
100
\frac{BC^2 + CA^2 + AB^2}{100}
100
B
C
2
+
C
A
2
+
A
B
2
.
median
geometry
perpendicular