← etc / Encyclopedia of Triangle Centers

X₄₆₈¶

X₂-LINE CONJUGATE OF X₃

X₄₆₈ = circumcircle-inverse of X₂₅

X₄₆₈ (X₂-LINE CONJUGATE OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_468 = X_2-LINE CONJUGATE OF X_3."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00468(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_468 = X_2-LINE CONJUGATE OF X_3 on reference triangle ABC."""
            X_468 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cot(B) + cot(C) - 2*cot(A))', ID="X_468", 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_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center", "incident"])
            X_231 = eval_trilinear_point(model, A, B, C, '(cos(B))*(4*(sin(C))**(2) - 1)*(cos(A)*sin(B) - sin(A)*cos(B)) - (cos(C))*(4*(sin(B))**(2) - 1)*(cos(C)*sin(A) - sin(C)*cos(A))', ID="X_231", classes=["center", "incident"])
            central_line(model, X_230, X_231, 230, 231, incident=True)
            X_250 = eval_trilinear_point(model, A, B, C, '(sec(A))*(csc(B - C))**(2)', ID="X_250", classes=["center", "incident"])
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center", "incident"])
            central_line(model, X_250, X_325, 250, 325, incident=True)
            return promote_point_to_top(model, X_468)


        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_468 on the given reference triangle."""
            model = create_model('X_468 = X_2-LINE CONJUGATE OF X_3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00468(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-00468.json"))
            write_center_svg(
                model_acute,
                here / "x-00468.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X468¶

X₄₆₈¶