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X₃₀₆₆¶

2nd LEMOINE HOMOTHETIC CENTER

This is a correction for trilinears given in TCCT, p. 188.

X₃₀₆₆ (2nd LEMOINE HOMOTHETIC CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3066 = 2nd LEMOINE HOMOTHETIC CENTER."""

        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,
            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_03066(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3066 = 2nd LEMOINE HOMOTHETIC CENTER on reference triangle ABC."""
            X_3066 = eval_trilinear_point(model, A, B, C, '(a*(a**(2) + 3*b**(2) - c**(2))*(a**(2) - b**(2) + 3*c**(2)))', ID="X_3066", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_6, X_110, 6, 110, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_25, X_182, 25, 182, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_373 = eval_trilinear_point(model, A, B, C, '(2*b*c + a*c*cos(C) + a*b*cos(B))', ID="X_373", classes=["center", "incident"])
            central_line(model, X_3, X_373, 3, 373, incident=True)
            return promote_point_to_top(model, X_3066)


        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_3066 on the given reference triangle."""
            model = create_model('X_3066 = 2nd LEMOINE HOMOTHETIC CENTER')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03066(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-03066.json"))
            write_center_svg(
                model_acute,
                here / "x-03066.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3066¶

X₃₀₆₆¶