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X₃₃₀₀¶

ISOGONAL CONJUGATE OF X₃₂₉₉

For a construction of the point X₃₃₀₀ see Ercole Suppa, euclid 5207.

X₃₃₀₀ (ISOGONAL CONJUGATE OF X₃₂₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3300 = ISOGONAL CONJUGATE OF X_3299."""

        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,
            incenter_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03300(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3300 = ISOGONAL CONJUGATE OF X_3299 on reference triangle ABC."""
            X_3299 = eval_trilinear_point(model, A, B, C, '1 + 2*sin(A)', ID="X_3299", classes=["center"])
            X_3300 = isogonal_conjugate(model, A, B, C, X_3299, ID="X_3300", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_615 = eval_trilinear_point(model, A, B, C, '(a**(2) - 4*area )/a', ID="X_615", classes=["center", "incident"])
            central_line(model, X_1, X_615, 1, 615, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_1373 = eval_trilinear_point(model, A, B, C, '1 + 8*( area )/(a*(b + c - a))', ID="X_1373", classes=["center", "incident"])
            central_line(model, X_57, X_1373, 57, 1373, incident=True)
            X_499 = eval_trilinear_point(model, A, B, C, '1 - 2*sin(B)*sin(C)', ID="X_499", classes=["center", "incident"])
            X_1123 = eval_trilinear_point(model, A, B, C, '1/(1 +sin(A))', ID="X_1123", classes=["center", "incident"])
            central_line(model, X_499, X_1123, 499, 1123, incident=True)
            return promote_point_to_top(model, X_3300)


        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_3300 on the given reference triangle."""
            model = create_model('X_3300 = ISOGONAL CONJUGATE OF X_3299')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03300(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-03300.json"))
            write_center_svg(
                model_acute,
                here / "x-03300.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3300¶

X₃₃₀₀¶