MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1962 All Russian Mathematical Olympiad
022
022
Part of
1962 All Russian Mathematical Olympiad
Problems
(1)
ASU 022 All Russian MO 1962 10.1 perpendicularity in isosceles
Source:
6/17/2019
The
M
M
M
point is the midpoint of the base
[
A
C
]
[AC]
[
A
C
]
of an isosceles triangle
A
B
C
ABC
A
BC
.
[
M
H
]
[MH]
[
M
H
]
is orthogonal to
[
B
C
]
[BC]
[
BC
]
side. Point
P
P
P
is the midpoint of the segment
[
M
H
]
[MH]
[
M
H
]
. Prove that
[
A
H
]
[AH]
[
A
H
]
is orthogonal to
[
B
P
]
[BP]
[
BP
]
.
geometry
isosceles
perpendicular