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Poland Contests
Polish MO Finals
1965 Polish MO Finals
5
5
Part of
1965 Polish MO Finals
Problems
(1)
triangle inscribed in triangle
Source: Polish MO Finals 1965 p5
8/30/2024
Points
A
1
A_1
A
1
,
B
1
B_1
B
1
,
C
1
C_1
C
1
divide respectively the sides
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
of the triangle
A
B
C
ABC
A
BC
in the ratios
k
1
k_1
k
1
,
k
2
k_2
k
2
,
k
3
k_3
k
3
. Calculate the ratio of the areas of triangles
A
1
B
1
C
1
A_1B_1C_1
A
1
B
1
C
1
and
A
B
C
ABC
A
BC
.
geometry
insscribed
areas