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X₃₁₅₁¶

X₃₀₆-CEVA CONJUGATE OF X₂

X₃₁₅₁ = reflection of X₂₇ in X₄₄₀

X₃₁₅₁ (X₃₀₆-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_3151 = X_306-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 (
            central_line,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03151(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3151 = X_306-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_27 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b + c)', ID="X_27", classes=["center"])
            X_440 = point_from_barycentrics(model, A, B, C, 0.44199278, 0.40077713, 0.15723009, ID="X_440", classes=["center"])
            X_3151 = reflection_in_point(model, X_27, X_440, ID="X_3151", classes=["selected", "target"], guide=False)
            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_306 = eval_trilinear_point(model, A, B, C, '(b**(2)*c**(2))*(b + c)*cos(A)', ID="X_306", classes=["center", "incident"])
            X_1330 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2)/(a + c) + c**(2)/(a + b) - a**(2)/(b + c)))', ID="X_1330", classes=["center", "incident"])
            central_line(model, X_306, X_1330, 306, 1330, incident=True)
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            X_1654 = eval_trilinear_point(model, A, B, C, '(b*c*(-a**(2) + b**(2) + c**(2) + b*c + c*a + a*b))', ID="X_1654", classes=["center", "incident"])
            central_line(model, X_71, X_1654, 71, 1654, incident=True)
            return promote_point_to_top(model, X_3151)


        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_3151 on the given reference triangle."""
            model = create_model('X_3151 = X_306-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03151(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-03151.json"))
            write_center_svg(
                model_acute,
                here / "x-03151.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3151¶

X₃₁₅₁¶