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X₃₅₈₆¶

INTERSECTION OF LINES X₁X_4 AND X₃₀X_57

X₃₅₈₆ = insimilicenter of hexyl and 2nd Johnson-Yff circles; the exsimilicenter is X₉₆₁₄

X₃₅₈₆ (INTERSECTION OF LINES X₁X_4 AND X₃₀X_57) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3586 = INTERSECTION OF LINES X_1X_4 AND X_30X_57."""

        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,
            mittenpunkt_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03586(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3586 = INTERSECTION OF LINES X_1X_4 AND X_30X_57 on reference triangle ABC."""
            X_3586 = eval_trilinear_point(model, A, B, C, '(b*c*(2*b**(4) + 2*c**(4) - 3*a**(4) + a**(3)*b + a**(3)*c - a*b**(3) - a*c**(3) + a**(2)*b**(2) + a**(2)*c**(2) + a*b*c*(b + c) + 2*a**(2)*b*c - 4*b**(2)*c**(2)))', ID="X_3586", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            central_line(model, X_1, X_4, 1, 4, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_30, X_57, 30, 57, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_9, X_80, 9, 80, incident=True)
            return promote_point_to_top(model, X_3586)


        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_3586 on the given reference triangle."""
            model = create_model('X_3586 = INTERSECTION OF LINES X_1X_4 AND X_30X_57')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03586(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-03586.json"))
            write_center_svg(
                model_acute,
                here / "x-03586.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3586¶

X₃₅₈₆¶