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X₇₄₂¶

EVEN (- 1, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₄₂ lies on the line at infinity.

X₇₄₂ (EVEN (- 1, 2) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_742 = EVEN (- 1, 2) INFINITY POINT."""

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


        def construct_x_00742(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_742 = EVEN (- 1, 2) INFINITY POINT on reference triangle ABC."""
            X_742 = eval_trilinear_point(model, A, B, C, '(a **(-2)*(b**(2) + c**(2)) - a**(1)*(b **(-1) + c **(-1)))', ID="X_742", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_6, X_75, 6, 75, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_37, X_141, 37, 141, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center", "incident"])
            central_line(model, X_69, X_192, 69, 192, incident=True)
            return promote_point_to_top(model, X_742)


        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_742 on the given reference triangle."""
            model = create_model('X_742 = EVEN (- 1, 2) INFINITY POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00742(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-00742.json"))
            write_center_svg(
                model_acute,
                here / "x-00742.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X742¶

X₇₄₂¶