← etc / Encyclopedia of Triangle Centers

X₃₂₁₀¶

X₅₇-CEVA CONJUGATE OF X₂

X₃₂₁₀ (X₅₇-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_3210 = X_57-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,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03210(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3210 = X_57-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center"])
            X_3210 = anticomplement(model, A, B, C, X_312, ID="X_3210", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_2, X_37, 2, 37, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            central_line(model, X_8, X_38, 8, 38, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_194 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*b**(2) + a**(2)*c**(2) - b**(2)*c**(2))', ID="X_194", classes=["center", "incident"])
            central_line(model, X_63, X_194, 63, 194, incident=True)
            return promote_point_to_top(model, X_3210)


        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_3210 on the given reference triangle."""
            model = create_model('X_3210 = X_57-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03210(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-03210.json"))
            write_center_svg(
                model_acute,
                here / "x-03210.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3210¶

X₃₂₁₀¶