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X₂₃₇¶

X₃-LINE CONJUGATE OF X₂

X₂₃₇ is the point of intersection of the Euler line and the Lemoine axis (defined as the radical axis of the circumcircle and the Brocard circle).

X₂₃₇ (X₃-LINE CONJUGATE OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_237 = X_3-LINE CONJUGATE OF X_2."""

        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_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00237(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_237 = X_3-LINE CONJUGATE OF X_2 on reference triangle ABC."""
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", 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_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_39, X_51, 39, 51, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_160 = eval_trilinear_point(model, A, B, C, '(a*((b**(2) + c**(2))*sin(2*A) + (c**(2) - a**(2))*sin(2*B) + (b**(2) - a**(2))*sin(2*C)))', ID="X_160", classes=["center", "incident"])
            central_line(model, X_6, X_160, 6, 160, incident=True)
            return promote_point_to_top(model, X_237)


        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_237 on the given reference triangle."""
            model = create_model('X_237 = X_3-LINE CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00237(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-00237.json"))
            write_center_svg(
                model_acute,
                here / "x-00237.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X237¶

X₂₃₇¶