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National and Regional Contests
South Africa Contests
South Africa National Olympiad
1999 South africa National Olympiad
2
2
Part of
1999 South africa National Olympiad
Problems
(1)
Construct the square...
Source: South Africa 1999
9/30/2005
A
,
B
,
C
A,\ B,\ C
A
,
B
,
C
and
D
D
D
are points on a given straight line, in that order. Show how to construct a square
P
Q
R
S
PQRS
PQRS
, with all of
P
,
Q
,
R
P,\ Q,\ R
P
,
Q
,
R
and
S
S
S
on the same side of
A
D
AD
A
D
, such that
A
,
B
,
C
A,\ B,\ C
A
,
B
,
C
and
D
D
D
lie on
P
Q
,
S
R
,
Q
R
PQ,\ SR,\ QR
PQ
,
SR
,
QR
and
P
S
PS
PS
produced respectively.