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Tuymaada Olympiad
1995 Tuymaada Olympiad
8
8
Part of
1995 Tuymaada Olympiad
Problems
(1)
min MP+PQ+QR+RM where M inside ABC, P,Q,R in AB,BC,CA resp
Source: Tuymaada 1995 p8
4/27/2019
Inside the triangle
A
B
C
ABC
A
BC
a point
M
M
M
is given . Find the points
P
,
Q
P,Q
P
,
Q
and
R
R
R
lying on the sides
A
B
,
B
C
AB,BC
A
B
,
BC
and
A
C
AC
A
C
respectively and such so that the sum
M
P
+
P
Q
+
Q
R
+
R
M
MP+PQ+QR+RM
MP
+
PQ
+
QR
+
RM
is the smallest.
geometry
geometric inequality
minimum
Sum
distance