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X₃₀₅₉¶

INTERSECTION OF LINES X₇X_8 AND X₉X_55

X₃₀₅₉ (INTERSECTION OF LINES X₇X_8 AND X₉X_55) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3059 = INTERSECTION OF LINES X_7X_8 AND X_9X_55."""

        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,
            cevapoint,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            incenter_of,
            mittenpunkt_of,
            nagel_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03059(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3059 = INTERSECTION OF LINES X_7X_8 AND X_9X_55 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2942 = point_from_barycentrics(model, A, B, C, 0.64126496, 0.51316479, -0.15442974, ID="X_2942", classes=["center"])
            X_3059 = cevapoint(model, A, B, C, X_1, X_2942, ID="X_3059", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_7, X_8, 7, 8, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            central_line(model, X_9, X_55, 9, 55, incident=True)
            X_142 = eval_trilinear_point(model, A, B, C, 'b + c - ((b - c)**(2))/a', ID="X_142", classes=["center", "incident"])
            X_354 = eval_trilinear_point(model, A, B, C, '(b - c)**(2) - a*b - a*c', ID="X_354", classes=["center", "incident"])
            central_line(model, X_142, X_354, 142, 354, incident=True)
            return promote_point_to_top(model, X_3059)


        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_3059 on the given reference triangle."""
            model = create_model('X_3059 = INTERSECTION OF LINES X_7X_8 AND X_9X_55')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03059(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-03059.json"))
            write_center_svg(
                model_acute,
                here / "x-03059.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3059¶

X₃₀₅₉¶