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South Africa Contests
South Africa National Olympiad
2002 South africa National Olympiad
3
3
Part of
2002 South africa National Olympiad
Problems
(1)
Funny problem with squares
Source: South Africa 2002
10/13/2005
A small square
P
Q
R
S
PQRS
PQRS
is contained in a big square. Produce
P
Q
PQ
PQ
to
A
A
A
,
Q
R
QR
QR
to
B
B
B
,
R
S
RS
RS
to
C
C
C
and
S
P
SP
SP
to
D
D
D
so that
A
A
A
,
B
B
B
,
C
C
C
and
D
D
D
lie on the four sides of the large square in order, produced if necessary. Prove that
A
C
=
B
D
AC = BD
A
C
=
B
D
and
A
C
⊥
B
D
AC \perp BD
A
C
⊥
B
D
.
geometry unsolved
geometry