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X₃₃₅₀¶

INTERSECTION OF LINES X₃X_2131 AND X₄X_1073

X₃₃₅₀ (INTERSECTION OF LINES X₃X_2131 AND X₄X_1073) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3350 = INTERSECTION OF LINES X_3X_2131 AND X_4X_1073."""

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


        def construct_x_03350(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3350 = INTERSECTION OF LINES X_3X_2131 AND X_4X_1073 on reference triangle ABC."""
            X_3349 = point_from_barycentrics(model, A, B, C, 0.30966513, 0.33289879, 0.35743608, ID="X_3349", classes=["center"])
            X_3350 = isogonal_conjugate(model, A, B, C, X_3349, ID="X_3350", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_1073 = eval_trilinear_point(model, A, B, C, '((cot(A))/(cos(A) - cos(B)*cos(C)))', ID="X_1073", classes=["center", "incident"])
            central_line(model, X_4, X_1073, 4, 1073, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_2131 = point_from_barycentrics(model, A, B, C, 0.36616655, 0.37250097, 0.26133249, ID="X_2131", classes=["center", "incident"])
            central_line(model, X_3, X_2131, 3, 2131, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_3344 = point_from_barycentrics(model, A, B, C, 0.41191386, 0.36788863, 0.22019751, ID="X_3344", classes=["center", "incident"])
            central_line(model, X_6, X_3344, 6, 3344, incident=True)
            return promote_point_to_top(model, X_3350)


        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_3350 on the given reference triangle."""
            model = create_model('X_3350 = INTERSECTION OF LINES X_3X_2131 AND X_4X_1073')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03350(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-03350.json"))
            write_center_svg(
                model_acute,
                here / "x-03350.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3350¶

X₃₃₅₀¶