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X₃₀₇₉¶

DANNEELS POINT OF X₂₀

X₃₀₇₉ (DANNEELS POINT OF X₂₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3079 = DANNEELS POINT OF X_20."""

        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,
            centroid_of,
            ceva_conjugate,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03079(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3079 = DANNEELS POINT OF X_20 on reference triangle ABC."""
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center"])
            X_1249 = eval_trilinear_point(model, A, B, C, '(tan(A))*(cos(A) - cos(B)*cos(C))', ID="X_1249", classes=["center"])
            X_3079 = ceva_conjugate(model, A, B, C, X_20, X_1249, ID="X_3079", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_154 = eval_trilinear_point(model, A, B, C, '(cos(A) - cos(B)*cos(C))*a**(2)', ID="X_154", classes=["center", "incident"])
            central_line(model, X_154, X_1249, 154, 1249, incident=True)
            X_204 = eval_trilinear_point(model, A, B, C, '((tan(A))*(tan(B) + tan(C) - tan(A)))', ID="X_204", classes=["center", "incident"])
            X_1394 = eval_trilinear_point(model, A, B, C, '(3*a**(4) - b**(4) - c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) + 2*b**(2)*c**(2))/(a - b - c)', ID="X_1394", classes=["center", "incident"])
            central_line(model, X_204, X_1394, 204, 1394, incident=True)
            return promote_point_to_top(model, X_3079)


        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_3079 on the given reference triangle."""
            model = create_model('X_3079 = DANNEELS POINT OF X_20')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03079(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-03079.json"))
            write_center_svg(
                model_acute,
                here / "x-03079.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3079¶

X₃₀₇₉¶