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X₂₉₄₀¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₅

X₂₉₄₀ is the excentral-isogonal conjugate of X₅.

X₂₉₄₀ (EXCENTRAL-ISOGONAL CONJUGATE OF X₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2940 = EXCENTRAL-ISOGONAL CONJUGATE OF X_5."""

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


        def construct_x_02940(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2940 = EXCENTRAL-ISOGONAL CONJUGATE OF X_5 on reference triangle ABC."""
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", 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"])
            X_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center"])
            central_line(model, X_35, X_37, 35, 37)
            central_line(model, X_191, X_210, 191, 210)
            X_2940 = intersect_lines(model, X_35, X_37, X_191, X_210, ID="X_2940", classes=["selected", "target"])
            X_484 = eval_trilinear_point(model, A, B, C, '1 + 2*(cos(A) - cos(B) - cos(C))', ID="X_484", classes=["center", "incident"])
            X_1046 = point_from_barycentrics(model, A, B, C, 0.13236391, 0.3064877, 0.5611484, ID="X_1046", classes=["center", "incident"])
            central_line(model, X_484, X_1046, 484, 1046, incident=True)
            return promote_point_to_top(model, X_2940)


        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_2940 on the given reference triangle."""
            model = create_model('X_2940 = EXCENTRAL-ISOGONAL CONJUGATE OF X_5')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02940(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-02940.json"))
            write_center_svg(
                model_acute,
                here / "x-02940.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2940¶

X₂₉₄₀¶