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X₃₁₈₇¶

X₂₇-CEVA CONJUGATE OF X₂

X₃₁₈₇ (X₂₇-CEVA CONJUGATE OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3187 = X_27-CEVA CONJUGATE OF X_2."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            anticomplement,
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03187(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3187 = X_27-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_306 = eval_trilinear_point(model, A, B, C, '(b**(2)*c**(2))*(b + c)*cos(A)', ID="X_306", classes=["center"])
            X_3187 = anticomplement(model, A, B, C, X_306, ID="X_3187", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            central_line(model, X_75, X_81, 75, 81, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_740 = eval_trilinear_point(model, A, B, C, 'a **(-2)*(b**(1) + c**(1)) - a**(0)*(b **(-1) + c **(-1))', ID="X_740", classes=["center", "incident"])
            central_line(model, X_31, X_740, 31, 740, incident=True)
            return promote_point_to_top(model, X_3187)


        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_3187 on the given reference triangle."""
            model = create_model('X_3187 = X_27-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03187(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-03187.json"))
            write_center_svg(
                model_acute,
                here / "x-03187.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3187¶

X₃₁₈₇¶