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X₃₇₅₆¶

X₁₀₆com[INVERSE(n(HEXYL TRIANGLE))]

X₃₇₅₆ = centroid of (degenerate) pedal triangle of X₁₀₆

X₃₇₅₆ (X₁₀₆com[INVERSE(n(HEXYL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3756 = X_106com[INVERSE(n(HEXYL TRIANGLE))]."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            feuerbach_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03756(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3756 = X_106com[INVERSE(n(HEXYL TRIANGLE))] on reference triangle ABC."""
            X_3756 = eval_barycentric_point(model, A, B, C, '((3*a - b - c)*(b - c)**(2))', ID="X_3756", classes=["selected", "target"])
            X_88 = eval_trilinear_point(model, A, B, C, '1/(b + c - 2*a)', ID="X_88", classes=["center", "incident"])
            X_149 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(3) + c**(3) - a**(3) + (a**(2) - b*c)*(b + c) + a*(b*c - b**(2) - c**(2))))', ID="X_149", classes=["center", "incident"])
            central_line(model, X_88, X_149, 88, 149, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            central_line(model, X_11, X_244, 11, 244, incident=True)
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            X_952 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a**(4) - 2*a**(3)*(b + c) - a**(2)*(b**(2) - 4*b*c + c**(2)) + (2*a - b - c)*(b - c)*(b**(2) - c**(2)))', ID="X_952", classes=["center", "incident"])
            central_line(model, X_106, X_952, 106, 952, incident=True)
            return promote_point_to_top(model, X_3756)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_3756 on the given reference triangle."""
            model = create_model('X_3756 = X_106com[INVERSE(n(HEXYL TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03756(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-03756.json"))
            write_center_svg(
                model_acute,
                here / "x-03756.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3756¶

X₃₇₅₆¶