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X₆₈₈¶

CROSSDIFFERENCE OF X₆ AND X₇₆

As the isogonal conjugate of a point on the circumcircle, X₆₈₈ lies on the line at infinity.

X₆₈₈ (CROSSDIFFERENCE OF X₆ AND X₇₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_688 = CROSSDIFFERENCE OF X_6 AND X_76."""

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


        def construct_x_00688(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_688 = CROSSDIFFERENCE OF X_6 AND X_76 on reference triangle ABC."""
            X_688 = eval_trilinear_point(model, A, B, C, '(a**(3)*(b**(4) - c**(4)))', ID="X_688", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_882 = point_from_barycentrics(model, A, B, C, 0.023590899, 1.0060979, -0.02968882, ID="X_882", classes=["center", "incident"])
            central_line(model, X_6, X_882, 6, 882, incident=True)
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["center", "incident"])
            X_864 = eval_trilinear_point(model, A, B, C, '((csc(C))**(3)*sin(2*B)*sin(C - A) + (csc(B))**(3)*sin(2*C)*sin(B - A))', ID="X_864", classes=["center", "incident"])
            central_line(model, X_669, X_864, 669, 864, incident=True)
            return promote_point_to_top(model, X_688)


        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_688 on the given reference triangle."""
            model = create_model('X_688 = CROSSDIFFERENCE OF X_6 AND X_76')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00688(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-00688.json"))
            write_center_svg(
                model_acute,
                here / "x-00688.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X688¶

X₆₈₈¶