← etc / Encyclopedia of Triangle Centers

X₃₁₆₇¶

X₆-CEVA CONJUGATE OF X₃

X₃₁₆₇ = Thomson-isogonal conjugate of X₂₀

X₃₁₆₇ (X₆-CEVA CONJUGATE OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3167 = X_6-CEVA 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03167(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3167 = X_6-CEVA CONJUGATE OF X_3 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center"])
            central_line(model, X_3, X_49, 3, 49)
            central_line(model, X_25, X_110, 25, 110)
            X_3167 = intersect_lines(model, X_3, X_49, X_25, X_110, ID="X_3167", classes=["selected", "target"])
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center", "incident"])
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center", "incident"])
            central_line(model, X_22, X_323, 22, 323, incident=True)
            return promote_point_to_top(model, X_3167)


        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_3167 on the given reference triangle."""
            model = create_model('X_3167 = X_6-CEVA CONJUGATE OF X_3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03167(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-03167.json"))
            write_center_svg(
                model_acute,
                here / "x-03167.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3167¶

X₃₁₆₇¶