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X₄₂₅¶

X₄-HIRST INVERSE OF X₂₁

X₄₂₅ (X₄-HIRST INVERSE OF X₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_425 = X_4-HIRST INVERSE OF X_21."""

        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,
            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_00425(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_425 = X_4-HIRST INVERSE OF X_21 on reference triangle ABC."""
            X_425 = eval_barycentric_point(model, A, B, C, '(a + b) * (a + c) * (a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(6) - a**(5)*b - a**(4)*b**(2) + a**(3)*b**(3) - a**(5)*c + a**(4)*b*c + a**(3)*b**(2)*c - b**(5)*c - a**(4)*c**(2) + a**(3)*b*c**(2) + 2*a**(2)*b**(2)*c**(2) - 2*a*b**(3)*c**(2) + a**(3)*c**(3) - 2*a*b**(2)*c**(3) + 2*b**(3)*c**(3) - b*c**(5))', ID="X_425", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_243 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(2) - cos(B)*cos(C))', ID="X_243", classes=["center", "incident"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            central_line(model, X_243, X_662, 243, 662, incident=True)
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            X_2707 = point_from_barycentrics(model, A, B, C, 1.0414086, 0.22924055, -0.27064911, ID="X_2707", classes=["center", "incident"])
            central_line(model, X_107, X_2707, 107, 2707, incident=True)
            return promote_point_to_top(model, X_425)


        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_425 on the given reference triangle."""
            model = create_model('X_425 = X_4-HIRST INVERSE OF X_21')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00425(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-00425.json"))
            write_center_svg(
                model_acute,
                here / "x-00425.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X425¶

X₄₂₅¶