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X₂₉₄₇¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₁₉

X₂₉₄₇ is the excentral-isogonal conjugate of X₁₉.

X₂₉₄₇ (EXCENTRAL-ISOGONAL CONJUGATE OF X₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2947 = EXCENTRAL-ISOGONAL CONJUGATE OF X_19."""

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


        def construct_x_02947(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2947 = EXCENTRAL-ISOGONAL CONJUGATE OF X_19 on reference triangle ABC."""
            X_219 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A/2)', ID="X_219", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2947 = ceva_conjugate(model, A, B, C, X_219, X_1, ID="X_2947", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            central_line(model, X_1, X_4, 1, 4, incident=True)
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            central_line(model, X_71, X_165, 71, 165, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_1754 = point_from_barycentrics(model, A, B, C, 0.042032164, 0.23903509, 0.71893275, ID="X_1754", classes=["center", "incident"])
            central_line(model, X_43, X_1754, 43, 1754, incident=True)
            return promote_point_to_top(model, X_2947)


        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_2947 on the given reference triangle."""
            model = create_model('X_2947 = EXCENTRAL-ISOGONAL CONJUGATE OF X_19')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02947(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-02947.json"))
            write_center_svg(
                model_acute,
                here / "x-02947.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2947¶

X₂₉₄₇¶