Steiner Inellipse is Unique

Theorem

For every triangle, there is one and only one Steiner inellipse.

Proof (outline)

Take your triangle and apply an affine transformation to map it to an equilateral triangle.

Inscribe an incircle in that equilateral triangle.

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A specific link is needed here. In particular: The incircle will touch the sides of the equilateral triangle at their midpoints. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by searching for it, and adding it here. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{LinkWanted}} from the code.

Perform the inverse affine transformation to map the equilateral triangle (complete with incircle) back to the triangle you started with.

By properties of affine transformations the circle will be a Steiner inellipse.

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