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X₂₉₁₂¶

ORTHIC-ISOGONAL CONJUGATE OF X₆₁

X₂₉₁₂ is the orthic-isogonal conjugate of X₆₁.

X₂₉₁₂ (ORTHIC-ISOGONAL CONJUGATE OF X₆₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2912 = ORTHIC-ISOGONAL CONJUGATE OF X_61."""

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


        def construct_x_02912(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2912 = ORTHIC-ISOGONAL CONJUGATE OF X_61 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_61 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /6)', ID="X_61", classes=["center"])
            X_2912 = ceva_conjugate(model, A, B, C, X_4, X_61, ID="X_2912", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_16 = eval_trilinear_point(model, A, B, C, 'sin(A-  pi  /3)', ID="X_16", classes=["center", "incident"])
            central_line(model, X_5, X_16, 5, 16, incident=True)
            X_143 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(2*C - 2*A) + cos(2*A - 2*B))', ID="X_143", classes=["center", "incident"])
            central_line(model, X_61, X_143, 61, 143, incident=True)
            X_62 = eval_trilinear_point(model, A, B, C, 'sin(A -  pi  /6)', ID="X_62", classes=["center", "incident"])
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            central_line(model, X_62, X_184, 62, 184, incident=True)
            return promote_point_to_top(model, X_2912)


        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_2912 on the given reference triangle."""
            model = create_model('X_2912 = ORTHIC-ISOGONAL CONJUGATE OF X_61')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02912(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-02912.json"))
            write_center_svg(
                model_acute,
                here / "x-02912.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2912¶

X₂₉₁₂¶