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X₃₈₃₁¶

X₃₇₀₂com(4th EULER TRIANGLE)

X₃₈₃₁ (X₃₇₀₂com(4th EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3831 = X_3702com(4th 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03831(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3831 = X_3702com(4th EULER TRIANGLE) on reference triangle ABC."""
            X_3831 = eval_barycentric_point(model, A, B, C, '(a**(2)*b**(2) + a**(2)*c**(2) + a*b**(3) + a*c**(3) + b**(3)*c + b*c**(3) + 2*b**(2)*c**(2))', ID="X_3831", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center", "incident"])
            X_986 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + b*c + c**(2)) + b**(3) + c**(3))', ID="X_986", classes=["center", "incident"])
            central_line(model, X_312, X_986, 312, 986, incident=True)
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            X_1329 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2)/(a - b + c) + c**(2)/(a + b - c)))', ID="X_1329", classes=["center", "incident"])
            central_line(model, X_141, X_1329, 141, 1329, incident=True)
            return promote_point_to_top(model, X_3831)


        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_3831 on the given reference triangle."""
            model = create_model('X_3831 = X_3702com(4th EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03831(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-03831.json"))
            write_center_svg(
                model_acute,
                here / "x-03831.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3831¶

X₃₈₃₁¶