← etc / Encyclopedia of Triangle Centers

X₃₁₉₁¶

X₂₉-CEVA CONJUGATE OF X₁₀

X₃₁₉₁ (X₂₉-CEVA CONJUGATE OF X₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3191 = X_29-CEVA CONJUGATE OF X_10."""

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


        def construct_x_03191(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3191 = X_29-CEVA CONJUGATE OF X_10 on reference triangle ABC."""
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center"])
            X_3191 = ceva_conjugate(model, A, B, C, X_29, X_10, ID="X_3191", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_28 = eval_trilinear_point(model, A, B, C, '(tan(A))/(b + c)', ID="X_28", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_28, X_101, 28, 101, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_228 = eval_trilinear_point(model, A, B, C, '(sin(2*A))*(sin(B) + sin(C))', ID="X_228", classes=["center", "incident"])
            central_line(model, X_40, X_228, 40, 228, incident=True)
            return promote_point_to_top(model, X_3191)


        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_3191 on the given reference triangle."""
            model = create_model('X_3191 = X_29-CEVA CONJUGATE OF X_10')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03191(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-03191.json"))
            write_center_svg(
                model_acute,
                here / "x-03191.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3191¶

X₃₁₉₁¶