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X₉₅₃¶

ISOGONAL CONJUGATE OF X₉₅₂

For a construction of X₉₅₃ involving the Euler line and X₁₁₀, see Antreas Hatzipolakis and César Lozada, Hyacinthos 26050.

X₉₅₃ (ISOGONAL CONJUGATE OF X₉₅₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_953 = ISOGONAL CONJUGATE OF X_952."""

        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,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00953(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_953 = ISOGONAL CONJUGATE OF X_952 on reference triangle ABC."""
            X_901 = eval_trilinear_point(model, A, B, C, 'a/((b - c)*(b + c - 2*a))', ID="X_901", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_953 = reflection_in_point(model, X_901, X_3, ID="X_953", classes=["selected", "target"], guide=False)
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_36, X_109, 36, 109, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center", "incident"])
            central_line(model, X_100, X_517, 100, 517, incident=True)
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_104, X_513, 104, 513, incident=True)
            return promote_point_to_top(model, X_953)


        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_953 on the given reference triangle."""
            model = create_model('X_953 = ISOGONAL CONJUGATE OF X_952')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00953(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-00953.json"))
            write_center_svg(
                model_acute,
                here / "x-00953.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X953¶

X₉₅₃¶