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X₉₂₈¶

CROSSDIFFERENCE OF X₆ AND X₁₁

As the isogonal conjugate of a point on the circumcircle, X₉₂₈ lies on the line at infinity.

X₉₂₈ (CROSSDIFFERENCE OF X₆ AND X₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_928 = CROSSDIFFERENCE OF X_6 AND X_11."""

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


        def construct_x_00928(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_928 = CROSSDIFFERENCE OF X_6 AND X_11 on reference triangle ABC."""
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center"])
            central_line(model, X_102, X_103, 102, 103)
            central_line(model, X_101, X_109, 101, 109)
            X_928 = intersect_lines(model, X_102, X_103, X_101, X_109, ID="X_928", classes=["selected", "target"])
            X_117 = point_from_barycentrics(model, A, B, C, 0.19223485, -0.017045455, 0.82481061, ID="X_117", classes=["center", "incident"])
            X_118 = point_from_barycentrics(model, A, B, C, 0.28918651, -0.056547619, 0.76736111, ID="X_118", classes=["center", "incident"])
            central_line(model, X_117, X_118, 117, 118, incident=True)
            return promote_point_to_top(model, X_928)


        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_928 on the given reference triangle."""
            model = create_model('X_928 = CROSSDIFFERENCE OF X_6 AND X_11')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00928(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-00928.json"))
            write_center_svg(
                model_acute,
                here / "x-00928.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X928¶

X₉₂₈¶