← etc / Encyclopedia of Triangle Centers

X₃₀₁₀¶

(LEMOINE AXIS)∩(SODDY LINE)

X₃₀₁₀ ((LEMOINE AXIS)∩(SODDY LINE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3010 = (LEMOINE AXIS)∩(SODDY LINE)."""

        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,
            gergonne_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03010(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3010 = (LEMOINE AXIS)∩(SODDY LINE) on reference triangle ABC."""
            X_3010 = eval_trilinear_point(model, A, B, C, '(a*b*((sec(A/2))**(2) - (sec(C/2))**(2)) + a*c*((sec(A/2))**(2) - (sec(B/2))**(2)))', ID="X_3010", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_1, X_7, 1, 7, incident=True)
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_1951 = eval_trilinear_point(model, A, B, C, 'a*((cos(A))**(2) - cos(B)*cos(C))', ID="X_1951", classes=["center", "incident"])
            central_line(model, X_31, X_1951, 31, 1951, incident=True)
            return promote_point_to_top(model, X_3010)


        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_3010 on the given reference triangle."""
            model = create_model('X_3010 = (LEMOINE AXIS)∩(SODDY LINE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03010(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-03010.json"))
            write_center_svg(
                model_acute,
                here / "x-03010.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3010¶

X₃₀₁₀¶