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X₃₈₃₂¶

X₃₀₉₀com(EULER TRIANGLE)

X₃₈₃₂ = {X₁₁₃₁,X₁₁₃₂}-harmonic conjugate of X₆

X₃₈₃₂ (X₃₀₉₀com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3832 = X_3090com(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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03832(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3832 = X_3090com(EULER TRIANGLE) on reference triangle ABC."""
            X_3832 = eval_barycentric_point(model, A, B, C, '(3*a**(4) - 5*b**(4) - 5*c**(4) + 2*a**(2)*b**(2) + 2*a**(2)*c**(2) + 10*b**(2)*c**(2))', ID="X_3832", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_390 = eval_trilinear_point(model, A, B, C, 'b*c*(b + c - a)*(3*a**(2) + (b - c)**(2))', ID="X_390", classes=["center", "incident"])
            central_line(model, X_12, X_390, 12, 390, incident=True)
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            X_946 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(3)*(b + c) + (b - c)**(2)*(a**(2) - a*b - a*c - b**(2) - c**(2) - 2*b*c))', ID="X_946", classes=["center", "incident"])
            central_line(model, X_145, X_946, 145, 946, incident=True)
            return promote_point_to_top(model, X_3832)


        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_3832 on the given reference triangle."""
            model = create_model('X_3832 = X_3090com(EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03832(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-03832.json"))
            write_center_svg(
                model_acute,
                here / "x-03832.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3832¶

X₃₈₃₂¶