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X₃₂₁₁¶

X₅₇-CEVA CONJUGATE OF X₃

X₃₂₁₁ = crosssum of X₆₅₀ and X₂₉₆₉

X₃₂₁₁ (X₅₇-CEVA CONJUGATE OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3211 = X_57-CEVA CONJUGATE OF X_3."""

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


        def construct_x_03211(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3211 = X_57-CEVA CONJUGATE OF X_3 on reference triangle ABC."""
            X_3211 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2) - a**(2))*(a**(4) - 2*a**(3)*(b + c) - 2*a**(2)*b*c + 2*a*(b**(3) + c**(3)) - (b**(2) - c**(2))**(2)))', ID="X_3211", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            central_line(model, X_3, X_48, 3, 48, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_169 = eval_trilinear_point(model, A, B, C, '- (sin(A))*(cos(A/2))**(2) + (sin(B))*(cos(B/2))**(2) + (sin(C))*(cos(C/2))**(2)', ID="X_169", classes=["center", "incident"])
            central_line(model, X_6, X_169, 6, 169, incident=True)
            X_155 = eval_trilinear_point(model, A, B, C, '(cos(A))*((cos(B))**(2) + (cos(C))**(2) - (cos(A))**(2))', ID="X_155", classes=["center", "incident"])
            X_610 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C) - tan(A)', ID="X_610", classes=["center", "incident"])
            central_line(model, X_155, X_610, 155, 610, incident=True)
            return promote_point_to_top(model, X_3211)


        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_3211 on the given reference triangle."""
            model = create_model('X_3211 = X_57-CEVA CONJUGATE OF X_3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03211(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-03211.json"))
            write_center_svg(
                model_acute,
                here / "x-03211.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3211¶

X₃₂₁₁¶