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National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2008.5
2008.5
Part of
Swiss NMO - geometry
Problems
(1)
locus of AP x CP + BPx DP = 1 where ABCD square of sidelength 1
Source: Switzerland - Swiss MO 2008 p5
7/17/2020
Let
A
B
C
D
ABCD
A
BC
D
be a square with side length
1
1
1
. Find the locus of all points
P
P
P
with the property
A
P
⋅
C
P
+
B
P
⋅
D
P
=
1
AP\cdot CP + BP\cdot DP = 1
A
P
⋅
CP
+
BP
⋅
D
P
=
1
.
geometry
Locus
square