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X₃₄₆₇¶

ISOGONAL CONJUGATE OF X₃₃₃₆

X₃₄₆₇ is the isogonal conjugate of X₃₃₃₆.

X₃₄₆₇ (ISOGONAL CONJUGATE OF X₃₃₃₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3467 = ISOGONAL CONJUGATE OF X_3336."""

        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,
            gergonne_point_of,
            incenter_of,
            isogonal_conjugate,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03467(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3467 = ISOGONAL CONJUGATE OF X_3336 on reference triangle ABC."""
            X_3336 = eval_trilinear_point(model, A, B, C, '(a - b + c)*(a + b - c)*(a + b + c) - a*b*c', ID="X_3336", classes=["center"])
            X_3467 = isogonal_conjugate(model, A, B, C, X_3336, ID="X_3467", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_79 = eval_trilinear_point(model, A, B, C, '1/(1 + 2*cos(A))', ID="X_79", classes=["center", "incident"])
            central_line(model, X_5, X_79, 5, 79, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_195 = eval_trilinear_point(model, A, B, C, 'a*(a**(8) + b**(8) + c**(8) - 4*a**(6)*(b**(2) + c**(2)) + a**(4)*(6*b**(4) + 6*c**(4) + 5*b**(2)*c**(2)) - a**(2)*(4*b**(6) + 4*c**(6) - b**(4)*c**(2) - b**(2)*c**(4)) - 2*b**(2)*c**(2)*(b**(4) + c**(4) - b**(2)*c**(2)))', ID="X_195", classes=["center", "incident"])
            central_line(model, X_1, X_195, 1, 195, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_499 = eval_trilinear_point(model, A, B, C, '1 - 2*sin(B)*sin(C)', ID="X_499", classes=["center", "incident"])
            central_line(model, X_7, X_499, 7, 499, incident=True)
            return promote_point_to_top(model, X_3467)


        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_3467 on the given reference triangle."""
            model = create_model('X_3467 = ISOGONAL CONJUGATE OF X_3336')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03467(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-03467.json"))
            write_center_svg(
                model_acute,
                here / "x-03467.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3467¶

X₃₄₆₇¶