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X₃₉₅₅¶

X₁₈₄₈com[INVERSE(n(ORTHIC TRIANGLE))]

X₃₉₅₅ = crosssum of the polar conjugates of PU(6)

X₃₉₅₅ (X₁₈₄₈com[INVERSE(n(ORTHIC TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3955 = X_1848com[INVERSE(n(ORTHIC TRIANGLE))]."""

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


        def construct_x_03955(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3955 = X_1848com[INVERSE(n(ORTHIC TRIANGLE))] on reference triangle ABC."""
            X_3955 = eval_barycentric_point(model, A, B, C, '(a**(2)*(a**(2) + b*c)*(b**(2) + c**(2) - a**(2)))', ID="X_3955", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_73 = eval_trilinear_point(model, A, B, C, 'sec(B) + sec(C)', ID="X_73", classes=["center", "incident"])
            central_line(model, X_3, X_73, 3, 73, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_57, X_182, 57, 182, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            central_line(model, X_63, X_184, 63, 184, incident=True)
            return promote_point_to_top(model, X_3955)


        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_3955 on the given reference triangle."""
            model = create_model('X_3955 = X_1848com[INVERSE(n(ORTHIC TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03955(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-03955.json"))
            write_center_svg(
                model_acute,
                here / "x-03955.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3955¶

X₃₉₅₅¶