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X₃₃₅₄¶

ISOGONAL CONJUGATE OF X₃₃₅₃

X₃₃₅₄ is the isogonal conjugate of X₃₃₅₃.

X₃₃₅₄ (ISOGONAL CONJUGATE OF X₃₃₅₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3354 = ISOGONAL CONJUGATE OF X_3353."""

        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,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03354(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3354 = ISOGONAL CONJUGATE OF X_3353 on reference triangle ABC."""
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center"])
            X_2130 = point_from_barycentrics(model, A, B, C, 0.19373197, 0.27423005, 0.53203798, ID="X_2130", classes=["center"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center"])
            X_3353 = point_from_barycentrics(model, A, B, C, 0.040677939, 0.071839896, 0.88748216, ID="X_3353", classes=["center"])
            central_line(model, X_40, X_2130, 40, 2130)
            central_line(model, X_20, X_3353, 20, 3353)
            X_3354 = intersect_lines(model, X_40, X_2130, X_20, X_3353, ID="X_3354", classes=["selected", "target"])
            X_1490 = eval_trilinear_point(model, A, B, C, '1 + sec(A) - sec(B) - sec(C)', ID="X_1490", classes=["center", "incident"])
            X_3183 = point_from_barycentrics(model, A, B, C, -0.24902136, -0.46731562, 1.716337, ID="X_3183", classes=["center", "incident"])
            central_line(model, X_1490, X_3183, 1490, 3183, incident=True)
            return promote_point_to_top(model, X_3354)


        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_3354 on the given reference triangle."""
            model = create_model('X_3354 = ISOGONAL CONJUGATE OF X_3353')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03354(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-03354.json"))
            write_center_svg(
                model_acute,
                here / "x-03354.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3354¶

X₃₃₅₄¶