32b. Construct a Triangle ABC Given the Length of AB, the Ratio of the Other Two Sides and a Line through C
32b. Construct a Triangle ABC Given the Length of AB, the Ratio of the Other Two Sides and a Line through C
This Demonstration shows the construction of a triangle given the length of the base , the ratio of the other two sides and a line containing .
ABC
c
AB
λ=b/a
μ
C
Construction
1. Draw a line and a line through and .
μ
σ
A
B
2. Draw the point such that . Draw the points and so that and is parallel to . Let be the point where and intersect. Let be the point where meets .
D
BD=a
H
I
AH=AI=b
HI
BD
F
DI
σ
E
DH
σ
3. Let be the midpoint of . Draw the circle with center and radius .
S
EF
κ
S
r=SF
4. The point is an intersection of and .
C
κ
μ
Verification
The circle is the Apollonius circle of the points and with respect to the ratio .
κ
A
B
λ=b/a