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X₃₆₂₄¶

H(X₁₀; M, 1/2)

X₃₆₂₄ = homothetic center of ABC and cross-triangle of Aquila and anti-Aquila triangles

X₃₆₂₄ (H(X₁₀; M, 1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3624 = H(X_10; M, 1/2)."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03624(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3624 = H(X_10; M, 1/2) on reference triangle ABC."""
            X_3624 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a +2*b + 2*c)', ID="X_3624", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center", "incident"])
            central_line(model, X_40, X_140, 40, 140, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_191 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(b*c + c*a + a*b) + b**(3) + c**(3) - a**(3)', ID="X_191", classes=["center", "incident"])
            central_line(model, X_57, X_191, 57, 191, incident=True)
            return promote_point_to_top(model, X_3624)


        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_3624 on the given reference triangle."""
            model = create_model('X_3624 = H(X_10; M, 1/2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03624(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-03624.json"))
            write_center_svg(
                model_acute,
                here / "x-03624.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3624¶

X₃₆₂₄¶