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X₁₅₁₉¶

ORTHOJOIN OF X₉

X₁₅₁₉ = orthopole of PU(96)

X₁₅₁₉ (ORTHOJOIN OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1519 = ORTHOJOIN OF X_9."""

        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,
            incenter_of,
            intersect_lines,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01519(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1519 = ORTHOJOIN OF X_9 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_119 = eval_trilinear_point(model, A, B, C, '(csc(A))*(-1 + cos(B) + cos(C))*(sin(2*B) + sin(2*C) + 2*(-1 + cos(A))*(sin(B) + sin(C)))', ID="X_119", classes=["center"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center"])
            central_line(model, X_1, X_4, 1, 4)
            central_line(model, X_119, X_517, 119, 517)
            X_1519 = intersect_lines(model, X_1, X_4, X_119, X_517, ID="X_1519", classes=["selected", "target"])
            X_499 = eval_trilinear_point(model, A, B, C, '1 - 2*sin(B)*sin(C)', ID="X_499", classes=["center", "incident"])
            X_1158 = eval_trilinear_point(model, A, B, C, 'a**(6) - b**(6) - c**(6) + b**(2)*c**(2)*(b**(2) + c**(2)) + 3*a**(2)*(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2)) + 2*a*b*c*(a**(3) - b**(3) - c**(3) - a*b*c + (a**(2) + b*c)*(b + c) - a*b**(2) - a*c**(2))', ID="X_1158", classes=["center", "incident"])
            central_line(model, X_499, X_1158, 499, 1158, incident=True)
            return promote_point_to_top(model, X_1519)


        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_1519 on the given reference triangle."""
            model = create_model('X_1519 = ORTHOJOIN OF X_9')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01519(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-01519.json"))
            write_center_svg(
                model_acute,
                here / "x-01519.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1519¶

X₁₅₁₉¶