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Problems
Contests
International Contests
Nordic
1990 Nordic
3
3
Part of
1990 Nordic
Problems
(1)
find line so that perimeter of a triangle is minimum
Source: Nordic Mathematical Contest 1990 #3
10/5/2017
Let
A
B
C
ABC
A
BC
be a triangle and let
P
P
P
be an interior point of
A
B
C
ABC
A
BC
. We assume that a line
l
l
l
, which passes through
P
P
P
, but not through
A
A
A
, intersects
A
B
AB
A
B
and
A
C
AC
A
C
(or their extensions over
B
B
B
or
C
C
C
) at
Q
Q
Q
and
R
R
R
, respectively. Find
l
l
l
such that the perimeter of the triangle
A
Q
R
AQR
A
QR
is as small as possible.
geometry