# 23. Construct a Triangle Given Two Sides and the Inradius

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.

[more]
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