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X₁₄₉₃¶

NAPOLEON CROSSSUM

X₁₄₉₃ = midpoint of X₅₄ and X₁₉₅

X₁₄₉₃ (NAPOLEON CROSSSUM) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1493 = NAPOLEON CROSSSUM."""

        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,
            midpoint,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01493(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1493 = NAPOLEON CROSSSUM on reference triangle ABC."""
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center"])
            X_195 = eval_trilinear_point(model, A, B, C, 'a*(a**(8) + b**(8) + c**(8) - 4*a**(6)*(b**(2) + c**(2)) + a**(4)*(6*b**(4) + 6*c**(4) + 5*b**(2)*c**(2)) - a**(2)*(4*b**(6) + 4*c**(6) - b**(4)*c**(2) - b**(2)*c**(4)) - 2*b**(2)*c**(2)*(b**(4) + c**(4) - b**(2)*c**(2)))', ID="X_195", classes=["center"])
            X_1493 = midpoint(model, X_54, X_195, ID="X_1493", classes=["selected", "target"], guide=False)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_3, X_54, 3, 54, incident=True)
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            X_143 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(2*C - 2*A) + cos(2*A - 2*B))', ID="X_143", classes=["center", "incident"])
            central_line(model, X_49, X_143, 49, 143, incident=True)
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            X_137 = point_from_barycentrics(model, A, B, C, 0.1354431, 0.64976082, 0.21479608, ID="X_137", classes=["center", "incident"])
            central_line(model, X_113, X_137, 113, 137, incident=True)
            return promote_point_to_top(model, X_1493)


        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_1493 on the given reference triangle."""
            model = create_model('X_1493 = NAPOLEON CROSSSUM')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01493(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-01493.json"))
            write_center_svg(
                model_acute,
                here / "x-01493.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1493¶

X₁₄₉₃¶