← etc / Encyclopedia of Triangle Centers

X₁₇₅₀¶

MIMOSA TRANSFORM OF X₂₆₈

X₁₇₅₀ (MIMOSA TRANSFORM OF X₂₆₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1750 = MIMOSA TRANSFORM OF X_268."""

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


        def construct_x_01750(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1750 = MIMOSA TRANSFORM OF X_268 on reference triangle ABC."""
            X_282 = eval_trilinear_point(model, A, B, C, '(cot(A/2))/(-1 - cos(A) + cos(B) + cos(C))', ID="X_282", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_1750 = ceva_conjugate(model, A, B, C, X_282, X_1, ID="X_1750", classes=["selected", "target"])
            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_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            central_line(model, X_9, X_165, 9, 165, 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_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center", "incident"])
            central_line(model, X_40, X_210, 40, 210, incident=True)
            return promote_point_to_top(model, X_1750)


        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_1750 on the given reference triangle."""
            model = create_model('X_1750 = MIMOSA TRANSFORM OF X_268')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01750(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-01750.json"))
            write_center_svg(
                model_acute,
                here / "x-01750.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1750¶

X₁₇₅₀¶