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X₁₀₂₃¶

INTERSECTION OF LINES X₁X_6 AND X₁₀₀X_101

X₁₀₂₃ = crossdifference of every pair of points on line X₂₄₄ X₅₁₃

X₁₀₂₃ (INTERSECTION OF LINES X₁X_6 AND X₁₀₀X_101) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1023 = INTERSECTION OF LINES X_1X_6 AND X_100X_101."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01023(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1023 = INTERSECTION OF LINES X_1X_6 AND X_100X_101 on reference triangle ABC."""
            X_1022 = eval_trilinear_point(model, A, B, C, '((b - c)/(2*a - b - c))', ID="X_1022", classes=["center"])
            X_1023 = isogonal_conjugate(model, A, B, C, X_1022, ID="X_1023", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_100, X_101, 100, 101, incident=True)
            X_813 = eval_trilinear_point(model, A, B, C, '1/(a**(-2)*(b**(1) - c**(1)) + a**(0)*(b**(-1) - c **(-1)))', ID="X_813", classes=["center", "incident"])
            X_898 = eval_trilinear_point(model, A, B, C, '1/((b - c)*(2*b*c - a*b - a*c))', ID="X_898", classes=["center", "incident"])
            central_line(model, X_813, X_898, 813, 898, incident=True)
            return promote_point_to_top(model, X_1023)


        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_1023 on the given reference triangle."""
            model = create_model('X_1023 = INTERSECTION OF LINES X_1X_6 AND X_100X_101')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01023(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-01023.json"))
            write_center_svg(
                model_acute,
                here / "x-01023.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1023¶

X₁₀₂₃¶