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X₂₉₆₁¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₂₀₀

X₂₉₆₁ is the excentral-isogonal conjugate of X₂₀₀.

X₂₉₆₁ (EXCENTRAL-ISOGONAL CONJUGATE OF X₂₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2961 = EXCENTRAL-ISOGONAL CONJUGATE OF X_200."""

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


        def construct_x_02961(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2961 = EXCENTRAL-ISOGONAL CONJUGATE OF X_200 on reference triangle ABC."""
            X_497 = eval_trilinear_point(model, A, B, C, '1 - cos(B)*cos(C)', ID="X_497", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2961 = ceva_conjugate(model, A, B, C, X_497, X_1, ID="X_2961", classes=["selected", "target"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            central_line(model, X_40, X_238, 40, 238, incident=True)
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            central_line(model, X_46, X_516, 46, 516, incident=True)
            X_1037 = eval_trilinear_point(model, A, B, C, '(1/(1 - cos(B)*cos(C)))', ID="X_1037", classes=["center", "incident"])
            central_line(model, X_1, X_1037, 1, 1037, incident=True)
            return promote_point_to_top(model, X_2961)


        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_2961 on the given reference triangle."""
            model = create_model('X_2961 = EXCENTRAL-ISOGONAL CONJUGATE OF X_200')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02961(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-02961.json"))
            write_center_svg(
                model_acute,
                here / "x-02961.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2961¶

X₂₉₆₁¶