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X₃₂₁₃¶

X₅₇-CEVA CONJUGATE OF X₃₄

X₃₂₁₃ (X₅₇-CEVA CONJUGATE OF X₃₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3213 = X_57-CEVA CONJUGATE OF X_34."""

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


        def construct_x_03213(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3213 = X_57-CEVA CONJUGATE OF X_34 on reference triangle ABC."""
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_1394 = eval_trilinear_point(model, A, B, C, '(3*a**(4) - b**(4) - c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) + 2*b**(2)*c**(2))/(a - b - c)', ID="X_1394", classes=["center"])
            X_3213 = crosspoint(model, A, B, C, X_57, X_1394, ID="X_3213", classes=["selected", "target"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            central_line(model, X_19, X_56, 19, 56, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_208 = eval_trilinear_point(model, A, B, C, '((1 - sec(A))*(cos(B) + cos(C) - cos(A) - 1))', ID="X_208", classes=["center", "incident"])
            central_line(model, X_6, X_208, 6, 208, incident=True)
            X_154 = eval_trilinear_point(model, A, B, C, '(cos(A) - cos(B)*cos(C))*a**(2)', ID="X_154", classes=["center", "incident"])
            X_204 = eval_trilinear_point(model, A, B, C, '((tan(A))*(tan(B) + tan(C) - tan(A)))', ID="X_204", classes=["center", "incident"])
            central_line(model, X_154, X_204, 154, 204, incident=True)
            return promote_point_to_top(model, X_3213)


        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_3213 on the given reference triangle."""
            model = create_model('X_3213 = X_57-CEVA CONJUGATE OF X_34')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03213(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-03213.json"))
            write_center_svg(
                model_acute,
                here / "x-03213.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3213¶

X₃₂₁₃¶