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X₉₆₉¶

INTERSECTION OF LINES X₁₀X_69 AND X₁₉X_81

X₉₆₉ (INTERSECTION OF LINES X₁₀X_69 AND X₁₉X_81) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_969 = INTERSECTION OF LINES X_10X_69 AND X_19X_81."""

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


        def construct_x_00969(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_969 = INTERSECTION OF LINES X_10X_69 AND X_19X_81 on reference triangle ABC."""
            X_968 = eval_trilinear_point(model, A, B, C, 'a**(2) - 2*a*(b + c) - (b + c)**(2)', ID="X_968", classes=["center"])
            X_969 = isogonal_conjugate(model, A, B, C, X_968, ID="X_969", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_10, X_69, 10, 69, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            central_line(model, X_19, X_81, 19, 81, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            central_line(model, X_37, X_63, 37, 63, incident=True)
            return promote_point_to_top(model, X_969)


        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_969 on the given reference triangle."""
            model = create_model('X_969 = INTERSECTION OF LINES X_10X_69 AND X_19X_81')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00969(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-00969.json"))
            write_center_svg(
                model_acute,
                here / "x-00969.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X969¶

X₉₆₉¶