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X₃₀₅₃¶

INTERSECTION X₃X_6∩X₄X_230

X₃₀₅₃ = inverse-in-circumcircle of X₁₆₉₂

X₃₀₅₃ (INTERSECTION X₃X_6∩X₄X_230) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3053 = INTERSECTION X_3X_6∩X_4X_230."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03053(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3053 = INTERSECTION X_3X_6∩X_4X_230 on reference triangle ABC."""
            X_2996 = eval_trilinear_point(model, A, B, C, '(b*c/(3*a**(2) - b**(2) - c**(2)))', ID="X_2996", classes=["center"])
            X_3053 = isogonal_conjugate(model, A, B, C, X_2996, ID="X_3053", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_24, X_112, 24, 112, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center", "incident"])
            central_line(model, X_4, X_230, 4, 230, incident=True)
            return promote_point_to_top(model, X_3053)


        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_3053 on the given reference triangle."""
            model = create_model('X_3053 = INTERSECTION X_3X_6∩X_4X_230')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03053(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-03053.json"))
            write_center_svg(
                model_acute,
                here / "x-03053.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3053¶

X₃₀₅₃¶