Basic Examples (1) 

Return an association containing the information of a partition of a given triangle into subtriangles sharing incircles of same size:

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Scope (3) 

Find a cevian partition of a given triangle into 7 triangle with incircles of same size:

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For each orientation, find a 4-part cevian partition:

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Certain triangles with integral sides also have integral inradii in a cevian triangle partition:

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Possible Issues (3) 

The number of partition must be at least 2. Otherwise the function returns unevaluated:

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Degenerate triangles are not supported. The function returns unevaluated:

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Perturb one vertex to create a non-degenerate case:

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Coordinates must be real numeric values. Otherwise the function returns unevaluated:

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Neat Examples (6) 

Given an arbitrary triangle, let n-1 cevians be drawn from one of its vertices so all of the n triangles so determined have equal incircles. Then the incircles determined by spanning 2, 3,…, n-1 adjacent triangles are also equal (Wells 1991, p. 67). For instance, a spanning set of size 2:

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Check the inradii:

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Visualize the cevian triangles and the incircles:

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Show the same result for spanning 3 adjacent intervals:

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The observation follows this general argument: in triangle TSR if two cevian triangles TSU and TVR have the same inradius, so do triangles TSV and TUR:

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Visually verify the argument:

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