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Hi,

I would like to understand how I can calculate the inner circle center of any equilateral triangle that has for constraint that each of its bissectors must intersect one extremity of the (for now lets assume bigger only) main triangle.

For helping understanding my problem and approach, imagine you have a disc with 3 variables legs extruding on the extremities of the disc, constrained such as they are distributed exactly at 120 deg one from each others on the disc (the legs of the real mechanical device I try to modelize also can rotate around their hinge point but lets consider only the 2d problem for now).

Now when all the legs have initially an exact same size ; their extremities form an equilateral triangle.

Then take an arbitrary case where the legs can have any size and you only have the input information of these extremities how to find out where the center of the disc was ?

I mocked up a viewer software application where I could easily visualize many experimentations to familiarize with the problem. As an example, I tried calculating different center points for the arbitrarily shaped triangle like : bissectors intersection, medians/barycentric coordinates, orthocenters and see if I could get equal angles (120 deg each) with some easy affine transformations, but didn't found out yet.

I'm not even sure that there is only one center point solution, should I approach the problem differently ?

TIA,

-Fab

I would like to understand how I can calculate the inner circle center of any equilateral triangle that has for constraint that each of its bissectors must intersect one extremity of the (for now lets assume bigger only) main triangle.

For helping understanding my problem and approach, imagine you have a disc with 3 variables legs extruding on the extremities of the disc, constrained such as they are distributed exactly at 120 deg one from each others on the disc (the legs of the real mechanical device I try to modelize also can rotate around their hinge point but lets consider only the 2d problem for now).

Now when all the legs have initially an exact same size ; their extremities form an equilateral triangle.

Then take an arbitrary case where the legs can have any size and you only have the input information of these extremities how to find out where the center of the disc was ?

I mocked up a viewer software application where I could easily visualize many experimentations to familiarize with the problem. As an example, I tried calculating different center points for the arbitrarily shaped triangle like : bissectors intersection, medians/barycentric coordinates, orthocenters and see if I could get equal angles (120 deg each) with some easy affine transformations, but didn't found out yet.

I'm not even sure that there is only one center point solution, should I approach the problem differently ?

TIA,

-Fab

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