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IMO Longlists
1982 IMO Longlists
6
6
Part of
1982 IMO Longlists
Problems
(1)
Construct Collinear Points X, Y, Z
Source: IMO LongList 1982 - P6
3/16/2011
On the three distinct lines
a
,
b
a, b
a
,
b
, and
c
c
c
three points
A
,
B
A, B
A
,
B
, and
C
C
C
are given, respectively. Construct three collinear points
X
,
Y
,
Z
X, Y,Z
X
,
Y
,
Z
on lines
a
,
b
,
c
a, b, c
a
,
b
,
c
, respectively, such that
B
Y
A
X
=
2
\frac{BY}{AX} = 2
A
X
B
Y
=
2
and
C
Z
A
X
=
3
\frac{CZ}{AX} = 3
A
X
CZ
=
3
.
geometry proposed
geometry