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X₃₁₂₅¶

DANNEELS PERSPECTOR FOR X₈₁

X₃₁₂₅ = cevapoint of X₂₆₄₃ and X₃₁₂₄

X₃₁₂₅ (DANNEELS PERSPECTOR FOR X₈₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3125 = DANNEELS PERSPECTOR FOR X_81."""

        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,
            cevapoint,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03125(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3125 = DANNEELS PERSPECTOR FOR X_81 on reference triangle ABC."""
            X_2643 = eval_trilinear_point(model, A, B, C, '1/(cot(C) - cot(A)) - 1/(cot(B) - cot(A))', ID="X_2643", classes=["center"])
            X_3124 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))**(2)', ID="X_3124", classes=["center"])
            X_3125 = cevapoint(model, A, B, C, X_2643, X_3124, ID="X_3125", classes=["selected", "target"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_115, X_125, 115, 125, incident=True)
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_213 = eval_trilinear_point(model, A, B, C, '(b + c)*a**(2)', ID="X_213", classes=["center", "incident"])
            central_line(model, X_65, X_213, 65, 213, incident=True)
            X_257 = eval_trilinear_point(model, A, B, C, '1/(a**(3) + a*b*c)', ID="X_257", classes=["center", "incident"])
            X_274 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c)', ID="X_274", classes=["center", "incident"])
            central_line(model, X_257, X_274, 257, 274, incident=True)
            return promote_point_to_top(model, X_3125)


        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_3125 on the given reference triangle."""
            model = create_model('X_3125 = DANNEELS PERSPECTOR FOR X_81')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03125(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-03125.json"))
            write_center_svg(
                model_acute,
                here / "x-03125.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3125¶

X₃₁₂₅¶