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X₁₂₅₇¶

ISOGONAL CONJUGATE OF X₁₁₀₄

X₁₂₅₇ is the isogonal conjugate of X₁₁₀₄.

X₁₂₅₇ (ISOGONAL CONJUGATE OF X₁₁₀₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1257 = ISOGONAL CONJUGATE OF X_1104."""

        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,
            isogonal_conjugate,
            nagel_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01257(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1257 = ISOGONAL CONJUGATE OF X_1104 on reference triangle ABC."""
            X_1104 = point_from_barycentrics(model, A, B, C, 0.17229255, 0.32067511, 0.50703235, ID="X_1104", classes=["center"])
            X_1257 = isogonal_conjugate(model, A, B, C, X_1104, ID="X_1257", classes=["selected", "target"])
            X_28 = eval_trilinear_point(model, A, B, C, '(tan(A))/(b + c)', ID="X_28", 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_28, X_72, 28, 72, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_78 = eval_trilinear_point(model, A, B, C, '1/(1 - sec(A))', ID="X_78", classes=["center", "incident"])
            central_line(model, X_57, X_78, 57, 78, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_278 = eval_trilinear_point(model, A, B, C, 'sec(A)*tan(A/2)', ID="X_278", classes=["center", "incident"])
            central_line(model, X_8, X_278, 8, 278, incident=True)
            return promote_point_to_top(model, X_1257)


        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_1257 on the given reference triangle."""
            model = create_model('X_1257 = ISOGONAL CONJUGATE OF X_1104')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01257(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-01257.json"))
            write_center_svg(
                model_acute,
                here / "x-01257.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1257¶

X₁₂₅₇¶