WOLFRAM|DEMONSTRATIONS PROJECT

18. Construct a Triangle Given the Length of Its Base, the Difference of Angles at Its Base and the Point of Intersection of an Angle Bisector with Its Base

​
c
1.4
D
0.6
δ
0.8
steps
1
2
3
4
This Demonstration shows a construction of a triangle
ABC
given the length
c
of its base
AB
, the difference
δ
of the base angles and the point
D
of intersection of the angle bisector
b
C
with the base
AB
.
Construction
Step 1: Draw a segment
AB
of length
c
and a point
D
on that segment.
Step 2: Construct the ray
σ
from
A
that forms the angle
δ/2
with
AB
and the ray
τ
from
D
that forms the angle
δ
with
AB
. Let
E
be the intersection of
σ
and
τ
.
Step 3: Draw a ray
ρ
from
D
at an angle
π/2+δ/2
from
AB
. The point
C
is the intersection of
ρ
with an extension of the segment
BE
.
Step 4: Triangle
ABC
is a solution of the problem.
Verification
The exterior angle of the triangle
DBE
at
E
is
α
. So
α=β+δ
,
δ=α-β
.