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X₃₈₂₇¶

X₅₁₈com(2nd EULER TRIANGLE)

X₃₈₂₇ = crossdifference of every pair of points on line X₆ X₅₂₁

X₃₈₂₇ (X₅₁₈com(2nd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3827 = X_518com(2nd EULER TRIANGLE)."""

        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_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03827(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3827 = X_518com(2nd EULER TRIANGLE) on reference triangle ABC."""
            X_3827 = eval_barycentric_point(model, A, B, C, '(a*(b**(5) + c**(5) - a**(4)*b - a**(4)*c - b**(4)*c - b*c**(4) + 2*a**(3)*b*c))', ID="X_3827", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            central_line(model, X_6, X_19, 6, 19, incident=True)
            X_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_66, X_72, 66, 72, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_159 = eval_trilinear_point(model, A, B, C, '(a*((a**(2) + b**(2) + c**(2))*sin(2*A) + (c**(2) - b**(2) - a**(2))*sin(2*B) + (b**(2) - c**(2) - a**(2))*sin(2*C)))', ID="X_159", classes=["center", "incident"])
            central_line(model, X_1, X_159, 1, 159, incident=True)
            return promote_point_to_top(model, X_3827)


        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_3827 on the given reference triangle."""
            model = create_model('X_3827 = X_518com(2nd EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03827(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-03827.json"))
            write_center_svg(
                model_acute,
                here / "x-03827.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3827¶

X₃₈₂₇¶