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X₃₁₄₇¶

X₂₅₄-CEVA CONJUGATE OF X₄

X₃₁₄₇ (X₂₅₄-CEVA CONJUGATE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3147 = X_254-CEVA CONJUGATE OF X_4."""

        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,
            centroid_of,
            ceva_conjugate,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03147(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3147 = X_254-CEVA CONJUGATE OF X_4 on reference triangle ABC."""
            X_254 = eval_trilinear_point(model, A, B, C, '(sec(A))/((cos(B))**(2) + (cos(C))**(2) - (cos(A))**(2))', ID="X_254", classes=["center"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_3147 = ceva_conjugate(model, A, B, C, X_254, X_4, ID="X_3147", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_1068 = eval_trilinear_point(model, A, B, C, '(1 - sec(A)*(cos(B) + cos(C)))', ID="X_1068", classes=["center", "incident"])
            X_1940 = eval_trilinear_point(model, A, B, C, '((sec(A))**(2) + sec(B)*sec(C))', ID="X_1940", classes=["center", "incident"])
            central_line(model, X_1068, X_1940, 1068, 1940, incident=True)
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center", "incident"])
            X_2904 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(4) + b**(4) + c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2))*(a**(6) - 3*a**(4)*(b**(2) + c**(2)) + 3*a**(2)*(b**(4) + c**(4)) - (b**(2) - c**(2))**(2)*(b**(2) + c**(2)))/(b**(2) + c**(2) - a**(2))', ID="X_2904", classes=["center", "incident"])
            central_line(model, X_323, X_2904, 323, 2904, incident=True)
            return promote_point_to_top(model, X_3147)


        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_3147 on the given reference triangle."""
            model = create_model('X_3147 = X_254-CEVA CONJUGATE OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03147(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-03147.json"))
            write_center_svg(
                model_acute,
                here / "x-03147.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3147¶

X₃₁₄₇¶