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X₃₃₄₅¶

ISOGONAL CONJUGATE OF X₁₄₉₀

X₃₃₄₅ is the isogonal conjugate of X₁₄₉₀.

X₃₃₄₅ (ISOGONAL CONJUGATE OF X₁₄₉₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3345 = ISOGONAL CONJUGATE OF X_1490."""

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


        def construct_x_03345(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3345 = ISOGONAL CONJUGATE OF X_1490 on reference triangle ABC."""
            X_3182 = point_from_barycentrics(model, A, B, C, -3.2427213, -5.3672014, 9.6099228, ID="X_3182", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_3345 = reflection_in_point(model, X_3182, X_3, ID="X_3345", classes=["selected", "target"], guide=False)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", 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_20, X_78, 20, 78, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_196 = eval_trilinear_point(model, A, B, C, '((cos(B) + cos(C) - cos(A) - 1)*sec(A)*tan(A/2))', ID="X_196", classes=["center", "incident"])
            central_line(model, X_1, X_196, 1, 196, incident=True)
            X_223 = eval_trilinear_point(model, A, B, C, '(tan(A/2))*(cos(B) + cos(C) - cos(A) - 1)', ID="X_223", classes=["center", "incident"])
            central_line(model, X_3, X_223, 3, 223, incident=True)
            return promote_point_to_top(model, X_3345)


        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_3345 on the given reference triangle."""
            model = create_model('X_3345 = ISOGONAL CONJUGATE OF X_1490')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03345(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-03345.json"))
            write_center_svg(
                model_acute,
                here / "x-03345.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3345¶

X₃₃₄₅¶