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X₁₀₀₉¶

INTERCEPT OF EULER LINE AND LINE X₁X_39

X₁₀₀₉ = crossdifference of every pair of points on line X₆₄₇ X₆₅₉

X₁₀₀₉ (INTERCEPT OF EULER LINE AND LINE X₁X_39) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1009 = INTERCEPT OF EULER LINE AND LINE X_1X_39."""

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


        def construct_x_01009(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1009 = INTERCEPT OF EULER LINE AND LINE X_1X_39 on reference triangle ABC."""
            X_1009 = eval_trilinear_point(model, A, B, C, '(a**(4)*(b + c) + 2*a**(3)*b*c - a**(2)*(b**(3) + c**(3)) + b*c*(b + c)*(b**(2) + c**(2)))', ID="X_1009", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_1, X_39, 1, 39, incident=True)
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_672 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) - a*(b + c))', ID="X_672", classes=["center", "incident"])
            central_line(model, X_72, X_672, 72, 672, incident=True)
            return promote_point_to_top(model, X_1009)


        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_1009 on the given reference triangle."""
            model = create_model('X_1009 = INTERCEPT OF EULER LINE AND LINE X_1X_39')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01009(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-01009.json"))
            write_center_svg(
                model_acute,
                here / "x-01009.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1009¶

X₁₀₀₉¶