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X₉₀₆¶

INTERSECTION OF LINES X₁₀₀X_112 AND X₁₀₁X_109

X₉₀₆ (INTERSECTION OF LINES X₁₀₀X_112 AND X₁₀₁X_109) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_906 = INTERSECTION OF LINES X_100X_112 AND X_101X_109."""

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


        def construct_x_00906(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_906 = INTERSECTION OF LINES X_100X_112 AND X_101X_109 on reference triangle ABC."""
            X_906 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(b - c)', ID="X_906", classes=["selected", "target"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_101, X_109, 101, 109, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_100, X_112, 100, 112, incident=True)
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_218 = eval_trilinear_point(model, A, B, C, '((cos(A/2))**(2)*((cos(B/2))**(4) + (cos(C/2))**(4) - (cos(A/2))**(4)))', ID="X_218", classes=["center", "incident"])
            central_line(model, X_32, X_218, 32, 218, incident=True)
            return promote_point_to_top(model, X_906)


        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_906 on the given reference triangle."""
            model = create_model('X_906 = INTERSECTION OF LINES X_100X_112 AND X_101X_109')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00906(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-00906.json"))
            write_center_svg(
                model_acute,
                here / "x-00906.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X906¶

X₉₀₆¶