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Brazil National Olympiad
1984 Brazil National Olympiad
4
4
Part of
1984 Brazil National Olympiad
Problems
(1)
minimum segment of projections of a point in hypotenuse on other sides
Source: Brazilian Mathematical Olympiad 1984 P4
7/27/2018
A
B
C
ABC
A
BC
is a triangle with
∠
A
=
9
0
o
\angle A = 90^o
∠
A
=
9
0
o
. For a point
D
D
D
on the side
B
C
BC
BC
, the feet of the perpendiculars to
A
B
AB
A
B
and
A
C
AC
A
C
are
E
E
E
and
F
F
F
. For which point
D
D
D
is
E
F
EF
EF
a minimum?
geometry
right triangle
minimum
projection
Segment