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X₃₀₄₇¶

INTERSECTION X₅₄X_113∩X₂X_98

X₃₀₄₇ = reflection of X₃₀₄₃ in X₄₉

X₃₀₄₇ (INTERSECTION X₅₄X_113∩X₂X_98) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3047 = INTERSECTION X_54X_113∩X_2X_98."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03047(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3047 = INTERSECTION X_54X_113∩X_2X_98 on reference triangle ABC."""
            X_3043 = eval_trilinear_point(model, A, B, C, '((1 - 4*(cos(A))**(2))**(2)*sec(A))', ID="X_3043", classes=["center"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center"])
            X_3047 = reflection_in_point(model, X_3043, X_49, ID="X_3047", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            central_line(model, X_2, X_98, 2, 98, incident=True)
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            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"])
            central_line(model, X_54, X_113, 54, 113, incident=True)
            X_156 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(8) - 3*a**(6)*(b**(2) + c**(2)) + a**(4)*(3*b**(4) + 2*b**(2)*c**(2) + 3*c**(4)) - a**(2)*(b**(6) + c**(6)) + b**(2)*c**(2)*(b**(2) - c**(2))**(2))', ID="X_156", classes=["center", "incident"])
            X_265 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*csc(3*A)', ID="X_265", classes=["center", "incident"])
            central_line(model, X_156, X_265, 156, 265, incident=True)
            return promote_point_to_top(model, X_3047)


        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_3047 on the given reference triangle."""
            model = create_model('X_3047 = INTERSECTION X_54X_113∩X_2X_98')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03047(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-03047.json"))
            write_center_svg(
                model_acute,
                here / "x-03047.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3047¶

X₃₀₄₇¶