← etc / Encyclopedia of Triangle Centers

X₃₁₈₁¶

X₁₄-CEVA CONJUGATE OF X₂

X₃₁₈₁ (X₁₄-CEVA CONJUGATE OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3181 = X_14-CEVA CONJUGATE OF X_2."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            anticomplement,
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03181(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3181 = X_14-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_299 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*sin(A -  pi  /3)', ID="X_299", classes=["center"])
            X_3181 = anticomplement(model, A, B, C, X_299, ID="X_3181", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_14 = eval_trilinear_point(model, A, B, C, 'csc(A -  pi  /3)', ID="X_14", classes=["center", "incident"])
            X_532 = point_from_barycentrics(model, A, B, C, -0.64045027, -0.11837216, 0.75882243, ID="X_532", classes=["center", "incident"])
            central_line(model, X_14, X_532, 14, 532, incident=True)
            X_16 = eval_trilinear_point(model, A, B, C, 'sin(A-  pi  /3)', ID="X_16", classes=["center", "incident"])
            X_533 = point_from_barycentrics(model, A, B, C, 0.76482932, -0.13487259, -0.62995674, ID="X_533", classes=["center", "incident"])
            central_line(model, X_16, X_533, 16, 533, incident=True)
            return promote_point_to_top(model, X_3181)


        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_3181 on the given reference triangle."""
            model = create_model('X_3181 = X_14-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03181(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-03181.json"))
            write_center_svg(
                model_acute,
                here / "x-03181.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3181¶

X₃₁₈₁¶