← etc / Encyclopedia of Triangle Centers

X₂₁₁¶

X₄-CEVA CONJUGATE OF X₃₉

X₂₁₁ (X₄-CEVA CONJUGATE OF X₃₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_211 = X_4-CEVA CONJUGATE OF X_39."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00211(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_211 = X_4-CEVA CONJUGATE OF X_39 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center"])
            X_211 = ceva_conjugate(model, A, B, C, X_4, X_39, ID="X_211", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_5, X_141, 5, 141, incident=True)
            X_52 = eval_trilinear_point(model, A, B, C, 'cos(2*A)*cos(B - C)', ID="X_52", classes=["center", "incident"])
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            central_line(model, X_52, X_114, 52, 114, incident=True)
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            central_line(model, X_32, X_184, 32, 184, incident=True)
            return promote_point_to_top(model, X_211)


        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_211 on the given reference triangle."""
            model = create_model('X_211 = X_4-CEVA CONJUGATE OF X_39')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00211(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-00211.json"))
            write_center_svg(
                model_acute,
                here / "x-00211.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X211¶

X₂₁₁¶