MathDB
Problems
Contests
International Contests
Nordic
1997 Nordic
3
3
Part of
1997 Nordic
Problems
(1)
4 points, 6 fixed equal distances, ratio of distances ?
Source: Nordic Mathematical Contest 1997 #3
10/4/2017
Let
A
,
B
,
C
A, B, C
A
,
B
,
C
, and
D
D
D
be four different points in the plane. Three of the line segments
A
B
,
A
C
,
A
D
,
B
C
,
B
D
AB, AC, AD, BC, BD
A
B
,
A
C
,
A
D
,
BC
,
B
D
, and
C
D
CD
C
D
have length
a
a
a
. The other three have length
b
b
b
, where
b
>
a
b > a
b
>
a
. Determine all possible values of the quotient
b
a
\frac{b}{a}
a
b
. .
ratio
distance
geometry
point set