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National and Regional Contests
Russia Contests
All-Russian Olympiad
1962 All-Soviet Union Olympiad
10
10
Part of
1962 All-Soviet Union Olympiad
Problems
(1)
Isosceles Triangle
Source: 1962 All-Soviet Union Olympiad
1/15/2018
In a triangle,
A
B
=
B
C
AB=BC
A
B
=
BC
and
M
M
M
is the midpoint of
A
C
AC
A
C
.
H
H
H
is chosen on
B
C
BC
BC
so that
M
H
MH
M
H
is perpendicular to
B
C
BC
BC
.
P
P
P
is the midpoint of
M
H
MH
M
H
. Prove that
A
H
AH
A
H
is perpendicular to
B
P
BP
BP
.
geometry
Russia