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National and Regional Contests
Vietnam Contests
Vietnam National Olympiad
1978 Vietnam National Olympiad
3
3
Part of
1978 Vietnam National Olympiad
Problems
(1)
minimize 5 PA + 4 PB + 3 PC, for P interior point of triangle
Source: Vietnam MO 1978 P3
7/29/2018
The triangle
A
B
C
ABC
A
BC
has angle
A
=
3
0
o
A = 30^o
A
=
3
0
o
and
A
B
=
3
4
A
C
AB = \frac{3}{4} AC
A
B
=
4
3
A
C
. Find the point
P
P
P
inside the triangle which minimizes
5
P
A
+
4
P
B
+
3
P
C
5 PA + 4 PB + 3 PC
5
P
A
+
4
PB
+
3
PC
.
geometry
minimum
Triangle