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Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine National Mathematical Olympiad
2021 Ukraine National Mathematical Olympiad
11.6
11.6
Part of
2021 Ukraine National Mathematical Olympiad
Problems
(1)
B symmedian bisects B_1k, 3 altitudes , projection of B
Source: 2021 Ukraine NMO 11.6
4/4/2021
The altitudes
A
A
1
,
B
B
1
AA_1, BB_1
A
A
1
,
B
B
1
and
C
C
1
CC_1
C
C
1
were drawn in the triangle
A
B
C
ABC
A
BC
. Point
K
K
K
is a projection of point
B
B
B
on
A
1
C
1
A_1C_1
A
1
C
1
. Prove that the symmmedian
△
A
B
C
\vartriangle ABC
△
A
BC
from the vertex
B
B
B
divides the segment
B
1
K
B_1K
B
1
K
in half.(Anton Trygub)
geometry
symmedian
bisects segment