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X₃₄₆₉¶

ISOGONAL CONJUGATE OF X₃₄₆₈

X₃₄₆₉ is the isogonal conjugate of X₃₄₆₈.

X₃₄₆₉ (ISOGONAL CONJUGATE OF X₃₄₆₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3469 = ISOGONAL CONJUGATE OF X_3468."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03469(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3469 = ISOGONAL CONJUGATE OF X_3468 on reference triangle ABC."""
            X_3468 = eval_trilinear_point(model, A, B, C, '2 - sec(A) + sec(B) + sec(C)', ID="X_3468", classes=["center"])
            X_3469 = isogonal_conjugate(model, A, B, C, X_3468, ID="X_3469", classes=["selected", "target"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            X_1745 = eval_trilinear_point(model, A, B, C, '(sec(B) + sec(C) - sec(A))', ID="X_1745", classes=["center", "incident"])
            central_line(model, X_77, X_1745, 77, 1745, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_3462 = point_from_barycentrics(model, A, B, C, 1.0069407, 1.1981673, -1.2051081, ID="X_3462", classes=["center", "incident"])
            central_line(model, X_1, X_3462, 1, 3462, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_3460 = point_from_barycentrics(model, A, B, C, 0.29060152, 0.26847785, 0.44092064, ID="X_3460", classes=["center", "incident"])
            central_line(model, X_3, X_3460, 3, 3460, incident=True)
            return promote_point_to_top(model, X_3469)


        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_3469 on the given reference triangle."""
            model = create_model('X_3469 = ISOGONAL CONJUGATE OF X_3468')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03469(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-03469.json"))
            write_center_svg(
                model_acute,
                here / "x-03469.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3469¶

X₃₄₆₉¶