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X₃₂₂₅¶

SS(a → bc) OF X₉₈

X₃₂₂₅ = Steiner-circumellipse-X₆-antipode of X₆₇₀

X₃₂₂₅ (SS(a → bc) OF X₉₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3225 = SS(a → bc) OF X_98."""

        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,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03225(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3225 = SS(a → bc) OF X_98 on reference triangle ABC."""
            X_3225 = eval_trilinear_point(model, A, B, C, '(b*c/(a**(2)*b**(4) + a**(2)*c**(4) - b**(2)*c**(4) - c **(2)*b**(4)))', ID="X_3225", classes=["selected", "target"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_32, X_99, 32, 99, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_670 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(2) - c**(2)))', ID="X_670", classes=["center", "incident"])
            central_line(model, X_6, X_670, 6, 670, incident=True)
            X_729 = eval_trilinear_point(model, A, B, C, '1/(a**(-3)*(b**(0) + c**(0)) - a **(-1)*(b**(-2) + c **(-2)))', ID="X_729", classes=["center", "incident"])
            X_886 = eval_barycentric_point(model, A, B, C, 'b**(2)*c**(2)/((b**(2) - c**(2))*(a**(2)*b**(2) + a**(2)*c**(2) - 2*b**(2)*c**(2)))', ID="X_886", classes=["center", "incident"])
            central_line(model, X_729, X_886, 729, 886, incident=True)
            return promote_point_to_top(model, X_3225)


        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_3225 on the given reference triangle."""
            model = create_model('X_3225 = SS(a → bc) OF X_98')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03225(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-03225.json"))
            write_center_svg(
                model_acute,
                here / "x-03225.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3225¶

X₃₂₂₅¶