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X₁₉₂₃¶

BICENTRIC SUM OF PU(13)

X₁₉₂₃ = crossdifference of every pair of points on line X₆₆₁ X₇₈₆

X₁₉₂₃ (BICENTRIC SUM OF PU(13)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1923 = BICENTRIC SUM OF PU(13)."""

        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,
            crosspoint,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01923(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1923 = BICENTRIC SUM OF PU(13) on reference triangle ABC."""
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center"])
            X_560 = eval_trilinear_point(model, A, B, C, 'a**(4)', ID="X_560", classes=["center"])
            X_1923 = crosspoint(model, A, B, C, X_31, X_560, ID="X_1923", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            central_line(model, X_1, X_21, 1, 21, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_719 = eval_trilinear_point(model, A, B, C, '(1/(a **(-4)*(b**(1) + c**(1)) - a**(0)*(b **(-3) + c **(-3))))', ID="X_719", classes=["center", "incident"])
            central_line(model, X_110, X_719, 110, 719, incident=True)
            return promote_point_to_top(model, X_1923)


        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_1923 on the given reference triangle."""
            model = create_model('X_1923 = BICENTRIC SUM OF PU(13)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01923(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-01923.json"))
            write_center_svg(
                model_acute,
                here / "x-01923.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1923¶

X₁₉₂₃¶