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X₃₄₉₉¶

INTERSECTION OF LINES X₃X_695 AND X₆X_76

X₃₄₉₉ (INTERSECTION OF LINES X₃X_695 AND X₆X_76) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3499 = INTERSECTION OF LINES X_3X_695 AND X_6X_76."""

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


        def construct_x_03499(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3499 = INTERSECTION OF LINES X_3X_695 AND X_6X_76 on reference triangle ABC."""
            X_3499 = eval_trilinear_point(model, A, B, C, '(a*(a**(4)*(b**(4) + b**(2)*c**(2) + c**(4)) + a**(2)*b**(2)*c**(2)*(b**(2) + c**(2)) - b**(4)*c**(4)))', ID="X_3499", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_6, X_76, 6, 76, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_695 = eval_trilinear_point(model, A, B, C, 'a/(a**(4) + b**(2)*c**(2))', ID="X_695", classes=["center", "incident"])
            central_line(model, X_3, X_695, 3, 695, incident=True)
            X_2076 = eval_trilinear_point(model, A, B, C, '(sin(A) - 2*cos(A)*sin(2*omega) )', ID="X_2076", classes=["center", "incident"])
            X_2916 = point_from_barycentrics(model, A, B, C, 0.54379762, 0.48047556, -0.024273171, ID="X_2916", classes=["center", "incident"])
            central_line(model, X_2076, X_2916, 2076, 2916, incident=True)
            return promote_point_to_top(model, X_3499)


        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_3499 on the given reference triangle."""
            model = create_model('X_3499 = INTERSECTION OF LINES X_3X_695 AND X_6X_76')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03499(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-03499.json"))
            write_center_svg(
                model_acute,
                here / "x-03499.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3499¶

X₃₄₉₉¶