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X₃₀₇₁¶

INTERSECTION OF X₄X_6 AND X₅X_371

X₃₀₇₁ (INTERSECTION OF X₄X_6 AND X₅X_371) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3071 = INTERSECTION OF X_4X_6 AND X_5X_371."""

        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,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03071(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3071 = INTERSECTION OF X_4X_6 AND X_5X_371 on reference triangle ABC."""
            X_489 = eval_trilinear_point(model, A, B, C, '((cos(A))*(1 - csc(A)*sin(B)*sin(C)) - cos(B)*cos(C))', ID="X_489", classes=["center"])
            X_3071 = complement(model, A, B, C, X_489, ID="X_3071", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_4, X_6, 4, 6, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_371 = eval_trilinear_point(model, A, B, C, 'cos(A -  pi  /4)', ID="X_371", classes=["center", "incident"])
            central_line(model, X_5, X_371, 5, 371, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_372 = eval_trilinear_point(model, A, B, C, 'cos(A +  pi  /4)', ID="X_372", classes=["center", "incident"])
            central_line(model, X_30, X_372, 30, 372, incident=True)
            return promote_point_to_top(model, X_3071)


        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_3071 on the given reference triangle."""
            model = create_model('X_3071 = INTERSECTION OF X_4X_6 AND X_5X_371')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03071(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-03071.json"))
            write_center_svg(
                model_acute,
                here / "x-03071.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3071¶

X₃₀₇₁¶