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X₁₀₀₄¶

INTERCEPT OF EULER LINE AND LINE X₇X_100

X₁₀₀₄ (INTERCEPT OF EULER LINE AND LINE X₇X_100) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1004 = INTERCEPT OF EULER LINE AND LINE X_7X_100."""

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


        def construct_x_01004(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1004 = INTERCEPT OF EULER LINE AND LINE X_7X_100 on reference triangle ABC."""
            X_1004 = eval_trilinear_point(model, A, B, C, 'a**(5) - 2*a**(4)*(b + c) + 2*a**(2)*(b**(3) + c**(3)) - a*(b**(2) + c**(2))**(2) + 2*b*c*(b - c)*(b**(2) - c**(2))', ID="X_1004", 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_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            central_line(model, X_7, X_100, 7, 100, incident=True)
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            X_200 = eval_trilinear_point(model, A, B, C, '(cot(A/2))**(2)', ID="X_200", classes=["center", "incident"])
            central_line(model, X_46, X_200, 46, 200, incident=True)
            return promote_point_to_top(model, X_1004)


        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_1004 on the given reference triangle."""
            model = create_model('X_1004 = INTERCEPT OF EULER LINE AND LINE X_7X_100')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01004(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-01004.json"))
            write_center_svg(
                model_acute,
                here / "x-01004.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1004¶

X₁₀₀₄¶