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X₃₅₀₅¶

INTERSECTION OF LINES X₃₂X_695 AND X₉₈X_783

X₃₅₀₅ (INTERSECTION OF LINES X₃₂X_695 AND X₉₈X_783) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3505 = INTERSECTION OF LINES X_32X_695 AND X_98X_783."""

        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_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03505(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3505 = INTERSECTION OF LINES X_32X_695 AND X_98X_783 on reference triangle ABC."""
            X_3505 = eval_trilinear_point(model, A, B, C, '(a*(b**(6) + c**(6) - a**(6) - a**(2)*b**(2)*c**(2))/(a**(4) + b**(2)*c**(2)))', ID="X_3505", classes=["selected", "target"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", 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_32, X_695, 32, 695, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_783 = eval_trilinear_point(model, A, B, C, '(1/(a **(-5)*(b**(4) - c**(4)) + a**(3)*(b **(-4) - c **(-4))))', ID="X_783", classes=["center", "incident"])
            central_line(model, X_98, X_783, 98, 783, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_3186 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2))/(b**(2) + c**(2) - a**(2)))', ID="X_3186", classes=["center", "incident"])
            central_line(model, X_2, X_3186, 2, 3186, incident=True)
            return promote_point_to_top(model, X_3505)


        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_3505 on the given reference triangle."""
            model = create_model('X_3505 = INTERSECTION OF LINES X_32X_695 AND X_98X_783')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03505(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-03505.json"))
            write_center_svg(
                model_acute,
                here / "x-03505.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3505¶

X₃₅₀₅¶