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Kvant 2020
M2590
M2590
Part of
Kvant 2020
Problems
(1)
Polyline divides triangle into equal figures
Source: Kvant Magazine No. 2 2020 M2590
3/10/2023
In an acute triangle
A
B
C
ABC
A
BC
the point
O
O{}
O
is the circumcenter,
H
1
H_1
H
1
is the foot of the perpendicular from
A
A{}
A
onto
B
C
BC
BC
, and
M
H
M_H
M
H
and
N
H
N_H
N
H
are the projections of
H
1
H_1
H
1
on
A
C
AC
A
C
and
A
B
AB{}
A
B
, respectively. Prove that the polyline
M
H
O
N
H
M_HON_H
M
H
O
N
H
divides the triangle
A
B
C
ABC
A
BC
in two figures of equal area.Proposed by I. A. Kushner
geometry
areas
Kvant