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X₂₄₈₆¶

RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE}

X₂₄₈₆ = intersection of tangents to nine-point circle at X₁₁ and X₁₁₅

X₂₄₈₆ (RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2486 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE}."""

        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,
            feuerbach_point_of,
            nine_point_center_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02486(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2486 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE} on reference triangle ABC."""
            X_2486 = eval_trilinear_point(model, A, B, C, '(b*c*(b - c)*((b**(2) - c**(2))*(a**(2) - b*c - c*a - a*b)))', ID="X_2486", classes=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            central_line(model, X_11, X_244, 11, 244, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_804 = eval_trilinear_point(model, A, B, C, 'a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))', ID="X_804", classes=["center", "incident"])
            central_line(model, X_115, X_804, 115, 804, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_2783 = point_from_barycentrics(model, A, B, C, -0.15779991, 0.77267542, -0.61487551, ID="X_2783", classes=["center", "incident"])
            central_line(model, X_5, X_2783, 5, 2783, incident=True)
            return promote_point_to_top(model, X_2486)


        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_2486 on the given reference triangle."""
            model = create_model('X_2486 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02486(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-02486.json"))
            write_center_svg(
                model_acute,
                here / "x-02486.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2486¶

X₂₄₈₆¶