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National and Regional Contests
Vietnam Contests
Vietnam National Olympiad
1979 Vietnam National Olympiad
3
3
Part of
1979 Vietnam National Olympiad
Problems
(1)
find a point so that ratio of areas = ratio of perimeters
Source: Vietnam MO 1979 P3
7/28/2018
A
B
C
ABC
A
BC
is a triangle. Find a point
X
X
X
on
B
C
BC
BC
such that : area
A
B
X
ABX
A
BX
/ area
A
C
X
ACX
A
CX
= perimeter
A
B
X
ABX
A
BX
/ perimeter
A
C
X
ACX
A
CX
.
geometry
perimeter
ratio