20. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Line Containing the Third Vertex
20. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Line Containing the Third Vertex
This Demonstration constructs a triangle given the length of its base, the difference of the base angles and a line that contains .
ABC
c
δ
λ
C
Introduce the Cartesian coordinate system with the base for the axis and the origin at the midpoint of the segment . The slope-intercept form of the line is determined by the angle it makes with \b\b and its intercept : the equation is .
AB
x
M
AB
λ
ϵ
AB
y
n
y=-tan(ϵ)x+n
Suppose that has coordinates and the coordinates of the circumcenter are . Let be the circumradius. The four independent conditions
C
(,)
x
1
y
1
S
(0,s)
R
1. is on
C
λ
2. is on
C
σ
3. =+
2
R
2
s
2
(c/2)
4. lies on the line through that forms an angle with
C
D
δ/2+π/2
AB
determine , , and .
x
1
x
2
s
R