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X₃₀₄₃¶

INTERSECTION X₄X_110∩X₇₄X_184

X₃₀₄₃ = reflection of X₃₀₄₇ in X₄₉

X₃₀₄₃ (INTERSECTION X₄X_110∩X₇₄X_184) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3043 = INTERSECTION X_4X_110∩X_74X_184."""

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


        def construct_x_03043(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3043 = INTERSECTION X_4X_110∩X_74X_184 on reference triangle ABC."""
            X_3043 = eval_trilinear_point(model, A, B, C, '((1 - 4*(cos(A))**(2))**(2)*sec(A))', ID="X_3043", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_4, X_110, 4, 110, incident=True)
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_54, X_125, 54, 125, incident=True)
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            central_line(model, X_74, X_184, 74, 184, incident=True)
            return promote_point_to_top(model, X_3043)


        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_3043 on the given reference triangle."""
            model = create_model('X_3043 = INTERSECTION X_4X_110∩X_74X_184')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03043(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-03043.json"))
            write_center_svg(
                model_acute,
                here / "x-03043.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3043¶

X₃₀₄₃¶