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X₁₅₇₈¶

POINT ALTERF I

X₁₅₇₈ = inverse-in-Brocard-circle of X₁₅₇₉

X₁₅₇₈ (POINT ALTERF I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1578 = POINT ALTERF I."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01578(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1578 = POINT ALTERF I on reference triangle ABC."""
            X_1578 = eval_trilinear_point(model, A, B, C, 'sin(A) + sec(B)*sec(C)', ID="X_1578", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            X_488 = eval_trilinear_point(model, A, B, C, '((cos(A))*(1 + csc(A)*sin(B)*sin(C)))', ID="X_488", classes=["center", "incident"])
            central_line(model, X_394, X_488, 394, 488, incident=True)
            X_485 = eval_trilinear_point(model, A, B, C, 'sec(A -  pi  /4)', ID="X_485", classes=["center", "incident"])
            X_1368 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2)/(a**(2) - b**(2) + c**(2)) + c**(2)/(a**(2) + b**(2) - c**(2)))', ID="X_1368", classes=["center", "incident"])
            central_line(model, X_485, X_1368, 485, 1368, incident=True)
            return promote_point_to_top(model, X_1578)


        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_1578 on the given reference triangle."""
            model = create_model('X_1578 = POINT ALTERF I')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01578(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-01578.json"))
            write_center_svg(
                model_acute,
                here / "x-01578.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1578¶

X₁₅₇₈¶