MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Novosibirsk Oral Olympiad in Geometry
2017 Novosibirsk Oral Olympiad in Geometry
3
3
Part of
2017 Novosibirsk Oral Olympiad in Geometry
Problems
(1)
broken line's length = perimeter of ABC (2017 Novosibirsk Oral Geo Oly 8-9 p3)
Source:
4/26/2021
Medians
A
A
1
,
B
B
1
,
C
C
1
AA_1, BB_1, CC_1
A
A
1
,
B
B
1
,
C
C
1
and altitudes
A
A
2
,
B
B
2
,
C
C
2
AA_2, BB_2, CC_2
A
A
2
,
B
B
2
,
C
C
2
are drawn in triangle
A
B
C
ABC
A
BC
. Prove that the length of the broken line
A
1
B
2
C
1
A
2
B
1
C
2
A
1
A_1B_2C_1A_2B_1C_2A_1
A
1
B
2
C
1
A
2
B
1
C
2
A
1
is equal to the perimeter of triangle
A
B
C
ABC
A
BC
.
geometry
perimeter