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X₃₉₀₅¶

X₆₂₆com[INVERSE(n(3rd EULER TRIANGLE))]

X₃₉₀₅ (X₆₂₆com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3905 = X_626com[INVERSE(n(3rd EULER 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_trilinear_point,
            incenter_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03905(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3905 = X_626com[INVERSE(n(3rd EULER TRIANGLE))] on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center"])
            X_712 = eval_trilinear_point(model, A, B, C, '(a **(-4)*(b **(-2) + c **(-2)) - a **(-3)*(b **(-3) + c **(-3)))', ID="X_712", classes=["center"])
            central_line(model, X_1, X_75, 1, 75)
            central_line(model, X_32, X_712, 32, 712)
            X_3905 = intersect_lines(model, X_1, X_75, X_32, X_712, ID="X_3905", classes=["selected", "target"])
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center", "incident"])
            X_2329 = point_from_barycentrics(model, A, B, C, 0.35982814, 0.34317938, 0.29699248, ID="X_2329", classes=["center", "incident"])
            central_line(model, X_192, X_2329, 192, 2329, incident=True)
            return promote_point_to_top(model, X_3905)


        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_3905 on the given reference triangle."""
            model = create_model('X_3905 = X_626com[INVERSE(n(3rd EULER TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03905(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-03905.json"))
            write_center_svg(
                model_acute,
                here / "x-03905.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3905¶

X₃₉₀₅¶