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X₃₄₁₆¶

ISOGONAL CONJUGATE OF X₃₄₁₅

X₃₄₁₆ is the isogonal conjugate of X₃₄₁₅.

X₃₄₁₆ (ISOGONAL CONJUGATE OF X₃₄₁₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3416 = ISOGONAL CONJUGATE OF X_3415."""

        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,
            midpoint,
            nagel_point_of,
            promote_point_to_top,
            spieker_center_of,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03416(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3416 = ISOGONAL CONJUGATE OF X_3415 on reference triangle ABC."""
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center"])
            X_3416 = midpoint(model, X_8, X_69, ID="X_3416", classes=["selected", "target"], guide=False)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_7, X_8, 7, 8, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            central_line(model, X_6, X_10, 6, 10, incident=True)
            X_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_66, X_72, 66, 72, incident=True)
            return promote_point_to_top(model, X_3416)


        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_3416 on the given reference triangle."""
            model = create_model('X_3416 = ISOGONAL CONJUGATE OF X_3415')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03416(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-03416.json"))
            write_center_svg(
                model_acute,
                here / "x-03416.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3416¶

X₃₄₁₆¶