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X₂₃₅₆¶

X₂-ISOCONJUGATE OF X₁₈₁₄

X₂₃₅₆ = crossdifference of every pair of points on line X₆₃ X₆₅₂

X₂₃₅₆ (X₂-ISOCONJUGATE OF X₁₈₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2356 = X_2-ISOCONJUGATE OF X_1814."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02356(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2356 = X_2-ISOCONJUGATE OF X_1814 on reference triangle ABC."""
            X_1861 = eval_barycentric_point(model, A, B, C, '(b**(2) + c**(2) - a*(b + c))/(a**(2) - b**(2) - c**(2))', ID="X_1861", classes=["center"])
            X_672 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) - a*(b + c))', ID="X_672", classes=["center"])
            X_2356 = ceva_conjugate(model, A, B, C, X_1861, X_672, ID="X_2356", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            central_line(model, X_1, X_4, 1, 4, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            central_line(model, X_25, X_41, 25, 41, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_459 = eval_trilinear_point(model, A, B, C, '(sec(A))/(tan(B) + tan(C) - tan(A))', ID="X_459", classes=["center", "incident"])
            central_line(model, X_43, X_459, 43, 459, incident=True)
            return promote_point_to_top(model, X_2356)


        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_2356 on the given reference triangle."""
            model = create_model('X_2356 = X_2-ISOCONJUGATE OF X_1814')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02356(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-02356.json"))
            write_center_svg(
                model_acute,
                here / "x-02356.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2356¶

X₂₃₅₆¶