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X₇₀¶

ISOGONAL CONJUGATE OF X₂₆

X₇₀ (ISOGONAL CONJUGATE OF X₂₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_70 = ISOGONAL CONJUGATE OF X_26."""

        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,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00070(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_70 = ISOGONAL CONJUGATE OF X_26 on reference triangle ABC."""
            X_26 = eval_trilinear_point(model, A, B, C, 'a*(b**(2)*cos(2*B) + c**(2)*cos(2*C) - a**(2)*cos(2*A))', ID="X_26", classes=["center"])
            X_70 = isogonal_conjugate(model, A, B, C, X_26, ID="X_70", classes=["selected", "target"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            X_1288 = point_from_barycentrics(model, A, B, C, -0.081215203, 0.1407786, 0.9404366, ID="X_1288", classes=["center", "incident"])
            central_line(model, X_74, X_1288, 74, 1288, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1594 = eval_trilinear_point(model, A, B, C, 'sec(A) + 2*cos(B - C)', ID="X_1594", classes=["center", "incident"])
            central_line(model, X_6, X_1594, 6, 1594, incident=True)
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_1899 = eval_trilinear_point(model, A, B, C, '2*b*c - a*b*sec(B) - a*c*sec(C)', ID="X_1899", classes=["center", "incident"])
            central_line(model, X_54, X_1899, 54, 1899, incident=True)
            return promote_point_to_top(model, X_70)


        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_70 on the given reference triangle."""
            model = create_model('X_70 = ISOGONAL CONJUGATE OF X_26')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00070(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-00070.json"))
            write_center_svg(
                model_acute,
                here / "x-00070.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X70¶

X₇₀¶