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X₃₁₉₈¶

X₄₀-CEVA CONJUGATE OF X₇₁

X₃₁₉₈ (X₄₀-CEVA CONJUGATE OF X₇₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3198 = X_40-CEVA CONJUGATE OF X_71."""

        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,
            crosspoint,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03198(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3198 = X_40-CEVA CONJUGATE OF X_71 on reference triangle ABC."""
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center"])
            X_610 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C) - tan(A)', ID="X_610", classes=["center"])
            X_3198 = crosspoint(model, A, B, C, X_20, X_610, ID="X_3198", classes=["selected", "target"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            central_line(model, X_19, X_25, 19, 25, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            central_line(model, X_40, X_64, 40, 64, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_42, X_65, 42, 65, incident=True)
            return promote_point_to_top(model, X_3198)


        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_3198 on the given reference triangle."""
            model = create_model('X_3198 = X_40-CEVA CONJUGATE OF X_71')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03198(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-03198.json"))
            write_center_svg(
                model_acute,
                here / "x-03198.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3198¶

X₃₁₉₈¶