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X₃₄₅₆¶

X₁₇-VERTEX CONJUGATE OF X₁₈

X₃₄₅₆ = crosssum of X₆₉ and X₁₃₆₉

X₃₄₅₆ (X₁₇-VERTEX CONJUGATE OF X₁₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3456 = X_17-VERTEX CONJUGATE OF X_18."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03456(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3456 = X_17-VERTEX CONJUGATE OF X_18 on reference triangle ABC."""
            X_3456 = eval_barycentric_point(model, A, B, C, 'a**(2)/(a**(4) - b**(4) - c**(4) - b**(2)*c**(2))', ID="X_3456", classes=["selected", "target"])
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center", "incident"])
            X_1799 = eval_trilinear_point(model, A, B, C, 'cot(A)*csc(A +  omega  )', ID="X_1799", classes=["center", "incident"])
            central_line(model, X_23, X_1799, 23, 1799, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_2916 = point_from_barycentrics(model, A, B, C, 0.54379762, 0.48047556, -0.024273171, ID="X_2916", classes=["center", "incident"])
            central_line(model, X_3, X_2916, 3, 2916, incident=True)
            return promote_point_to_top(model, X_3456)


        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_3456 on the given reference triangle."""
            model = create_model('X_3456 = X_17-VERTEX CONJUGATE OF X_18')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03456(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-03456.json"))
            write_center_svg(
                model_acute,
                here / "x-03456.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3456¶

X₃₄₅₆¶