Function Repository Resource:

MalfattiCircles

Construct the Malfatti circles of a triangle

Contributed by: Minh Trinh Xuan

ResourceFunction["MalfattiCircles"][{p₁,p₂,p₃}]

constructs the Malfatti circles of the triangle with corner points p₁,p₂, and p₃.

Details

The three Malfatti circles of a triangle are tangent to the sides of the triangle and each other.

ResourceFunction["MalfattiCircles"][Triangle[{p₁,p₂,p₃}]] is equivalent to ResourceFunction["MalfattiCircles"][{p₁,p₂,p₃}].

Find the Malfatti circles of a triangle:

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Show the circles:

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Find the Malfatti circles of a Triangle object:

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Malfatti circles with integer coordinates and radii:

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The inradius of a triangle can be expressed in terms of the radii of the Malfatti circles:

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Show the Malfatti circles of an arbitrary triangle in a Manipulate:

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Iteratively form the Malfatti circles of the triangle formed by the centers of the excircles:

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