MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Stanford Mathematics Tournament
2019 Stanford Mathematics Tournament
8
8
Part of
2019 Stanford Mathematics Tournament
Problems
(1)
SMT 2019 Geometry #8
Source:
8/8/2023
In the coordinate plane, a point
A
A
A
is chosen on the line
y
=
3
2
x
y =\frac32 x
y
=
2
3
x
in the first quadrant. Two perpendicular lines
ℓ
1
\ell_1
ℓ
1
and
ℓ
2
\ell_2
ℓ
2
intersect at A where
ℓ
1
\ell_1
ℓ
1
has slope
m
>
1
m > 1
m
>
1
. Let
ℓ
1
\ell_1
ℓ
1
intersect the
x
x
x
-axis at
B
B
B
, and
ℓ
2
\ell_2
ℓ
2
intersects the
x
x
x
and
y
y
y
axes at
C
C
C
and
D
D
D
, respectively. Suppose that line
B
D
BD
B
D
has slope
−
m
-m
−
m
and
B
D
=
2
BD = 2
B
D
=
2
. Compute the length of
C
D
CD
C
D
.
geometry