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Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2017 Junior Balkan Team Selection Tests - Moldova
Problem 7
Problem 7
Part of
2017 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
Perpendicularity
Source: Moldova JTST 2017, problem 7
5/3/2017
Given is an acute triangle
A
B
C
ABC
A
BC
and the median
A
M
.
AM.
A
M
.
Draw
B
H
⊥
A
C
.
BH\perp AC.
B
H
⊥
A
C
.
The line which goes through
A
A
A
and is perpendicular to
A
M
AM
A
M
intersects
B
H
BH
B
H
at
E
.
E.
E
.
On the opposite ray of the ray
A
E
AE
A
E
choose
F
F
F
such that
A
E
=
A
F
.
AE=AF.
A
E
=
A
F
.
Prove that
C
F
⊥
A
B
.
CF\perp AB.
CF
⊥
A
B
.
geometry