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X₁₂₄₂¶

ISOGONAL CONJUGATE OF X₁₀₀₅

X₁₂₄₂ is the isogonal conjugate of X₁₀₀₅.

X₁₂₄₂ (ISOGONAL CONJUGATE OF X₁₀₀₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1242 = ISOGONAL CONJUGATE OF X_1005."""

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


        def construct_x_01242(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1242 = ISOGONAL CONJUGATE OF X_1005 on reference triangle ABC."""
            X_1005 = point_from_barycentrics(model, A, B, C, 0.38047896, 0.36259614, 0.2569249, ID="X_1005", classes=["center"])
            X_1242 = isogonal_conjugate(model, A, B, C, X_1005, ID="X_1242", classes=["selected", "target"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_527 = eval_barycentric_point(model, A, B, C, '2*a**(2) - a*(b + c) - (b - c)**(2)', ID="X_527", classes=["center", "incident"])
            central_line(model, X_72, X_527, 72, 527, incident=True)
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            X_1155 = eval_trilinear_point(model, A, B, C, '(cos(B) + cos(C) - 2*cos(A))', ID="X_1155", classes=["center", "incident"])
            central_line(model, X_71, X_1155, 71, 1155, incident=True)
            return promote_point_to_top(model, X_1242)


        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_1242 on the given reference triangle."""
            model = create_model('X_1242 = ISOGONAL CONJUGATE OF X_1005')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01242(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-01242.json"))
            write_center_svg(
                model_acute,
                here / "x-01242.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1242¶

X₁₂₄₂¶