26c. Construct a Triangle Given the Length of Its Base, the Angle Opposite the Base and the Length of That Angle's Bisector

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This Demonstration constructs a triangle given the length
of its base
, the angle
at the point
, and the length of the angle bisector at
. The Demonstration uses the conchoid of Nicomedes, which is shown in red.
Contributed by: Izidor Hafner (October 2017)
Open content licensed under CC BY-NC-SA
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Details
The base of a conchoid is a straight line . Let
(the pole of the conchoid) be a point not on the base such that the distance of
from
is
. Let
be a ray from
not parallel to the base. The ray
intersects the base at a point
. Measure out points
and
on the ray so that
, where
is a positive number. The conchoid determined by the base, the pole and
is the set of all such points
and
.
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