# 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