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X₂₉₀₈¶

ORTHIC-ISOGONAL CONJUGATE OF X₃₁

X₂₉₀₈ is the orthic-isogonal conjugate of X₃₁.

X₂₉₀₈ (ORTHIC-ISOGONAL CONJUGATE OF X₃₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2908 = ORTHIC-ISOGONAL CONJUGATE OF X_31."""

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


        def construct_x_02908(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2908 = ORTHIC-ISOGONAL CONJUGATE OF X_31 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center"])
            X_2908 = ceva_conjugate(model, A, B, C, X_4, X_31, ID="X_2908", classes=["selected", "target"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            central_line(model, X_37, X_48, 37, 48, incident=True)
            X_604 = eval_trilinear_point(model, A, B, C, 'a*(1 - cos(A))', ID="X_604", classes=["center", "incident"])
            X_1015 = eval_trilinear_point(model, A, B, C, 'a*(b - c)**(2)', ID="X_1015", classes=["center", "incident"])
            central_line(model, X_604, X_1015, 604, 1015, incident=True)
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            X_2092 = eval_trilinear_point(model, A, B, C, '(a**(2)*(b + c)**(2) + a*(b + c)*(b**(2) + c**(2)))', ID="X_2092", classes=["center", "incident"])
            central_line(model, X_41, X_2092, 41, 2092, incident=True)
            return promote_point_to_top(model, X_2908)


        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_2908 on the given reference triangle."""
            model = create_model('X_2908 = ORTHIC-ISOGONAL CONJUGATE OF X_31')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02908(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-02908.json"))
            write_center_svg(
                model_acute,
                here / "x-02908.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2908¶

X₂₉₀₈¶