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X₆₅₃¶

TRILINEAR POLE OF LINE X₁X_4

X₆₅₃ = polar conjugate of X₅₂₂

X₆₅₃ (TRILINEAR POLE OF LINE X₁X_4) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_653 = TRILINEAR POLE OF LINE X_1X_4."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00653(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_653 = TRILINEAR POLE OF LINE X_1X_4 on reference triangle ABC."""
            X_652 = eval_trilinear_point(model, A, B, C, 'sec(B) - sec(C)', ID="X_652", classes=["center"])
            X_653 = isogonal_conjugate(model, A, B, C, X_652, ID="X_653", classes=["selected", "target"])
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_29, X_65, 29, 65, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_57, X_92, 57, 92, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_196 = eval_trilinear_point(model, A, B, C, '((cos(B) + cos(C) - cos(A) - 1)*sec(A)*tan(A/2))', ID="X_196", classes=["center", "incident"])
            central_line(model, X_2, X_196, 2, 196, incident=True)
            return promote_point_to_top(model, X_653)


        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_653 on the given reference triangle."""
            model = create_model('X_653 = TRILINEAR POLE OF LINE X_1X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00653(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-00653.json"))
            write_center_svg(
                model_acute,
                here / "x-00653.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X653¶

X₆₅₃¶