← etc / Encyclopedia of Triangle Centers

X₁₇₂₉¶

MIMOSA TRANSFORM OF X₈₅

X₁₇₂₉ (MIMOSA TRANSFORM OF X₈₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1729 = MIMOSA TRANSFORM OF X_85."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            mittenpunkt_of,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01729(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1729 = MIMOSA TRANSFORM OF X_85 on reference triangle ABC."""
            X_331 = eval_trilinear_point(model, A, B, C, '(sec(A/2))**(2)*csc(2*A)', ID="X_331", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_1729 = ceva_conjugate(model, A, B, C, X_331, X_1, ID="X_1729", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            central_line(model, X_5, X_9, 5, 9, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_169 = eval_trilinear_point(model, A, B, C, '- (sin(A))*(cos(A/2))**(2) + (sin(B))*(cos(B/2))**(2) + (sin(C))*(cos(C/2))**(2)', ID="X_169", classes=["center", "incident"])
            central_line(model, X_63, X_169, 63, 169, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_1158 = eval_trilinear_point(model, A, B, C, 'a**(6) - b**(6) - c**(6) + b**(2)*c**(2)*(b**(2) + c**(2)) + 3*a**(2)*(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2)) + 2*a*b*c*(a**(3) - b**(3) - c**(3) - a*b*c + (a**(2) + b*c)*(b + c) - a*b**(2) - a*c**(2))', ID="X_1158", classes=["center", "incident"])
            central_line(model, X_19, X_1158, 19, 1158, incident=True)
            return promote_point_to_top(model, X_1729)


        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_1729 on the given reference triangle."""
            model = create_model('X_1729 = MIMOSA TRANSFORM OF X_85')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01729(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-01729.json"))
            write_center_svg(
                model_acute,
                here / "x-01729.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1729¶

X₁₇₂₉¶