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X₂₉₄₉¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₃₅

X₂₉₄₉ is the excentral-isogonal conjugate of X₃₅.

X₂₉₄₉ (EXCENTRAL-ISOGONAL CONJUGATE OF X₃₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2949 = EXCENTRAL-ISOGONAL CONJUGATE OF X_35."""

        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_trilinear_point,
            incenter_of,
            intersect_lines,
            mittenpunkt_of,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02949(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2949 = EXCENTRAL-ISOGONAL CONJUGATE OF X_35 on reference triangle ABC."""
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_191 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(b*c + c*a + a*b) + b**(3) + c**(3) - a**(3)', ID="X_191", classes=["center"])
            central_line(model, X_5, X_9, 5, 9)
            central_line(model, X_4, X_191, 4, 191)
            X_2949 = intersect_lines(model, X_5, X_9, X_4, X_191, ID="X_2949", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_201 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(B - C))', ID="X_201", classes=["center", "incident"])
            central_line(model, X_1, X_201, 1, 201, incident=True)
            return promote_point_to_top(model, X_2949)


        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_2949 on the given reference triangle."""
            model = create_model('X_2949 = EXCENTRAL-ISOGONAL CONJUGATE OF X_35')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02949(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-02949.json"))
            write_center_svg(
                model_acute,
                here / "x-02949.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2949¶

X₂₉₄₉¶