20. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Line Containing the Third Vertex

c

1

δ

0.8

ϵ

1

MP

-0.07

plot range

1

given δ	calculated α - β
0.8	-0.341593

This Demonstration constructs a triangle

ABC

given the length

c

of its base, the difference

δ

of the base angles and a line

λ

that contains

C

.

Introduce the Cartesian coordinate system with the base

AB

for the

x

axis and the origin at the midpoint

M

of the segment

AB

. The slope-intercept form of the line

λ

is determined by the angle

ϵ

it makes with

AB

\b\b and its

y

intercept

n

: the equation is

y=-tan(ϵ)x+n

.

Suppose that

C

has coordinates

(

x

1

,

y

1

)

and the coordinates of the circumcenter

S

are

(0,s)

. Let

R

be the circumradius. The four independent conditions

1.

C

is on

λ

2.

C

is on

σ

3.

2

R

=

2

s

+

2

(c/2)

4.

C

lies on the line through

D

that forms an angle

δ/2+π/2

with

AB

determine

x

1

,

x

2

,

s

and

R

.