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X₃₄₆₈¶

X₅-CEVA CONJUGATE OF X₃₃₃₆

X₃₄₆₈ (X₅-CEVA CONJUGATE OF X₃₃₃₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3468 = X_5-CEVA CONJUGATE OF X_3336."""

        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,
            incenter_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03468(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3468 = X_5-CEVA CONJUGATE OF X_3336 on reference triangle ABC."""
            X_3468 = eval_trilinear_point(model, A, B, C, '2 - sec(A) + sec(B) + sec(C)', ID="X_3468", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            central_line(model, X_1, X_4, 1, 4, incident=True)
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            X_1410 = point_from_barycentrics(model, A, B, C, 0.21489592, 0.38593986, 0.39916422, ID="X_1410", classes=["center", "incident"])
            central_line(model, X_36, X_1410, 36, 1410, incident=True)
            X_62 = eval_trilinear_point(model, A, B, C, 'sin(A -  pi  /6)', ID="X_62", classes=["center", "incident"])
            X_1652 = eval_trilinear_point(model, A, B, C, '(sqrt(3/4) - sin(A +  pi  /3) + sin(B +  pi  /3) + sin(C +  pi  /3))', ID="X_1652", classes=["center", "incident"])
            central_line(model, X_62, X_1652, 62, 1652, incident=True)
            return promote_point_to_top(model, X_3468)


        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_3468 on the given reference triangle."""
            model = create_model('X_3468 = X_5-CEVA CONJUGATE OF X_3336')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03468(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-03468.json"))
            write_center_svg(
                model_acute,
                here / "x-03468.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3468¶

X₃₄₆₈¶