23. Construct a Triangle Given Two Sides and the Inradius
![](/img/demonstrations-branding.png)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration draws a triangle given two side lengths
and
and the inradius
(the radius of the inscribed circle). This construction involves solving a cubic and is not possible with a ruler and compass.
Contributed by: Izidor Hafner (November 2017)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The case ,
,
gives
, where
. Substitute
to get
.
Since the leading coefficient of the equation is , a rational root would have to be an integer that divides 32. But no integer
,
,
,
,
,
,
,
,
,
is a root of the equation. Therefore the last equation in
(and so also the first in
) has no rational solutions.
According to the theorem on p. 42 of [1], none of the roots can be constructed by ruler and compass, but the roots can be constructed using a marked ruler [1, p. 134].
Reference
[1] G. E. Martin, Geometric Constructions, New York: Springer, 1998.
Permanent Citation