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X₃₅₇₈¶

INTERSECTION OF LINES X₂X_6 AND X₈X_30

X₃₅₇₈ (INTERSECTION OF LINES X₂X_6 AND X₈X_30) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3578 = INTERSECTION OF LINES X_2X_6 AND X_8X_30."""

        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,
            centroid_of,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03578(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3578 = INTERSECTION OF LINES X_2X_6 AND X_8X_30 on reference triangle ABC."""
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center"])
            X_1125 = eval_trilinear_point(model, A, B, C, '(2*a+b+c)/a', ID="X_1125", classes=["center"])
            X_3578 = ceva_conjugate(model, A, B, C, X_75, X_1125, ID="X_3578", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            central_line(model, X_8, X_30, 8, 30, incident=True)
            X_340 = eval_trilinear_point(model, A, B, C, 'sec(A)*sin(3*A)*(csc(A))**(3)', ID="X_340", classes=["center", "incident"])
            X_445 = eval_barycentric_point(model, A, B, C, '(a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) - b*c - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(2)*b - b**(3) + a**(2)*c + 2*a*b*c + b**(2)*c + b*c**(2) - c**(3))', ID="X_445", classes=["center", "incident"])
            central_line(model, X_340, X_445, 340, 445, incident=True)
            return promote_point_to_top(model, X_3578)


        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_3578 on the given reference triangle."""
            model = create_model('X_3578 = INTERSECTION OF LINES X_2X_6 AND X_8X_30')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03578(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-03578.json"))
            write_center_svg(
                model_acute,
                here / "x-03578.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3578¶

X₃₅₇₈¶