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National and Regional Contests
Greece Contests
Greece National Olympiad
1997 Greece National Olympiad
1
1
Part of
1997 Greece National Olympiad
Problems
(1)
Extrema for a function defined on a square
Source: Greek national M.O. 1997, Final Round, problem 1
11/20/2011
Let
P
P
P
be a point inside or on the boundary of a square
A
B
C
D
ABCD
A
BC
D
. Find the minimum and maximum values of
f
(
P
)
=
∠
A
B
P
+
∠
B
C
P
+
∠
C
D
P
+
∠
D
A
P
f(P ) = \angle ABP + \angle BCP + \angle CDP + \angle DAP
f
(
P
)
=
∠
A
BP
+
∠
BCP
+
∠
C
D
P
+
∠
D
A
P
.
function
geometry unsolved
geometry