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WOLFRAM|DEMONSTRATIONS PROJECT

32b. Construct a Triangle ABC Given the Length of AB, the Ratio of the Other Two Sides and a Line through C

​
move B
1.3
λ
a
1.2
b
0.66
line with point C
y intercept
1
slope
0.7
change D
1.4
steps
1
2
3
4
plot range
1.4
This Demonstration shows the construction of a triangle
ABC
given the length
c
of the base
AB
, the ratio
λ=b/a
of the other two sides and a line
μ
containing
C
.
Construction
1. Draw a line
μ
and a line
σ
through
A
and
B
.
2. Draw the point
D
such that
BD=a
. Draw the points
H
and
I
so that
AH=AI=b
and
HI
is parallel to
BD
. Let
F
be the point where
DI
and
σ
intersect. Let
E
be the point where
DH
meets
σ
.
3. Let
S
be the midpoint of
EF
. Draw the circle
κ
with center
S
and radius
r=SF
.
4. The point
C
is an intersection of
κ
and
μ
.
Verification
The circle
κ
is the Apollonius circle of the points
A
and
B
with respect to the ratio
λ=b/a
.
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