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X₃₁₀₈¶

DC(X₈₃)

For an introduction to the DC and CD mappings, see the discussion just before X₂₉₇₉.

X₃₁₀₈ (DC(X₈₃)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3108 = DC(X_83)."""

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


        def construct_x_03108(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3108 = DC(X_83) on reference triangle ABC."""
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center"])
            X_251 = eval_trilinear_point(model, A, B, C, 'a**(2)*csc(A +  omega  )', ID="X_251", classes=["center"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center"])
            X_1180 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) + b**(2)*c**(2) + c**(2)*a**(2) + a**(2)*b**(2))', ID="X_1180", classes=["center"])
            central_line(model, X_39, X_251, 39, 251)
            central_line(model, X_25, X_1180, 25, 1180)
            X_3108 = intersect_lines(model, X_39, X_251, X_25, X_1180, ID="X_3108", classes=["selected", "target"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            X_1194 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) + a**(2)*b**(2) + a**(2)*c**(2)))', ID="X_1194", classes=["center", "incident"])
            central_line(model, X_111, X_1194, 111, 1194, incident=True)
            return promote_point_to_top(model, X_3108)


        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_3108 on the given reference triangle."""
            model = create_model('X_3108 = DC(X_83)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03108(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-03108.json"))
            write_center_svg(
                model_acute,
                here / "x-03108.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3108¶

X₃₁₀₈¶