← etc / Encyclopedia of Triangle Centers

X₂₀₉¶

X₄-CEVA CONJUGATE OF X₃₇

X₂₀₉ (X₄-CEVA CONJUGATE OF X₃₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_209 = X_4-CEVA CONJUGATE OF X_37."""

        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,
            promote_point_to_top,
            spieker_center_of,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00209(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_209 = X_4-CEVA CONJUGATE OF X_37 on reference triangle ABC."""
            X_209 = eval_trilinear_point(model, A, B, C, '((sin(B) + sin(C))*(sin(A) + sin(A - B) + sin(A - C)))', ID="X_209", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_10, X_12, 10, 12, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            central_line(model, X_6, X_31, 6, 31, incident=True)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_44, X_51, 44, 51, incident=True)
            return promote_point_to_top(model, X_209)


        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_209 on the given reference triangle."""
            model = create_model('X_209 = X_4-CEVA CONJUGATE OF X_37')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00209(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-00209.json"))
            write_center_svg(
                model_acute,
                here / "x-00209.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X209¶

X₂₀₉¶