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X₃₀₃₀¶

INTERSECTION X₁₀X_11∩X₄₃X_57

X₃₀₃₀ = reflection of X₁₃₅₇ in X₁₀₅₄

X₃₀₃₀ (INTERSECTION X₁₀X_11∩X₄₃X_57) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3030 = INTERSECTION X_10X_11∩X_43X_57."""

        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,
            feuerbach_point_of,
            promote_point_to_top,
            reflection_in_point,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03030(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3030 = INTERSECTION X_10X_11∩X_43X_57 on reference triangle ABC."""
            X_1357 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)*(b - c)**(2)*(a**(2) - (b - c)**(2))**(2)', ID="X_1357", classes=["center"])
            X_1054 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2) - a**(2) - 3*b*c + a*b + a*c', ID="X_1054", classes=["center"])
            X_3030 = reflection_in_point(model, X_1357, X_1054, ID="X_3030", classes=["selected", "target"], guide=False)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_10, X_11, 10, 11, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_43, X_57, 43, 57, incident=True)
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            X_386 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_386", classes=["center", "incident"])
            central_line(model, X_106, X_386, 106, 386, incident=True)
            return promote_point_to_top(model, X_3030)


        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_3030 on the given reference triangle."""
            model = create_model('X_3030 = INTERSECTION X_10X_11∩X_43X_57')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03030(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-03030.json"))
            write_center_svg(
                model_acute,
                here / "x-03030.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3030¶

X₃₀₃₀¶