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X₁₄₇₅¶

X₁₂₁₂-BETH CONJUGATE OF X₁₂₁₂

X₁₄₇₅ (X₁₂₁₂-BETH CONJUGATE OF X₁₂₁₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1475 = X_1212-BETH CONJUGATE OF X_1212."""

        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,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01475(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1475 = X_1212-BETH CONJUGATE OF X_1212 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center"])
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center"])
            central_line(model, X_6, X_41, 6, 41)
            central_line(model, X_39, X_42, 39, 42)
            X_1475 = intersect_lines(model, X_6, X_41, X_39, X_42, ID="X_1475", classes=["selected", "target"])
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center", "incident"])
            central_line(model, X_58, X_163, 58, 163, incident=True)
            return promote_point_to_top(model, X_1475)


        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_1475 on the given reference triangle."""
            model = create_model('X_1475 = X_1212-BETH CONJUGATE OF X_1212')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01475(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-01475.json"))
            write_center_svg(
                model_acute,
                here / "x-01475.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1475¶

X₁₄₇₅¶