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X₁₁₅₄¶

ISOGONAL CONJUGATE OF X₁₁₄₁

X₁₁₅₄ is the isogonal conjugate of X₁₁₄₁.

X₁₁₅₄ (ISOGONAL CONJUGATE OF X₁₁₄₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1154 = ISOGONAL CONJUGATE OF X_1141."""

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


        def construct_x_01154(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1154 = ISOGONAL CONJUGATE OF X_1141 on reference triangle ABC."""
            X_1141 = eval_trilinear_point(model, A, B, C, 'b*c/(16*D**(2) + (a**(2)+c**(2)-b**(2))*(a**(2)+b**(2)-c**(2)))*(16*D**(2) - 3*(b**(2)+c**(2)-a**(2))**(2))', ID="X_1141", classes=["center"])
            X_1154 = isogonal_conjugate(model, A, B, C, X_1141, ID="X_1154", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_5, X_51, 5, 51, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            central_line(model, X_3, X_54, 3, 54, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_93 = eval_trilinear_point(model, A, B, C, 'sec(3*A)', ID="X_93", classes=["center", "incident"])
            central_line(model, X_4, X_93, 4, 93, incident=True)
            return promote_point_to_top(model, X_1154)


        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_1154 on the given reference triangle."""
            model = create_model('X_1154 = ISOGONAL CONJUGATE OF X_1141')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01154(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-01154.json"))
            write_center_svg(
                model_acute,
                here / "x-01154.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1154¶

X₁₁₅₄¶