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X₁₇₆₉¶

MIMOSA TRANSFORM OF X₉₀₁

X₁₇₆₉ = trilinear product of circumcircle intercepts of Sherman line

X₁₇₆₉ (MIMOSA TRANSFORM OF X₉₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1769 = MIMOSA TRANSFORM OF X_901."""

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


        def construct_x_01769(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1769 = MIMOSA TRANSFORM OF X_901 on reference triangle ABC."""
            X_1769 = eval_trilinear_point(model, A, B, C, '(b - c)*(a**(2)*(b + c) - 2*a*b*c - (b - c)**(2)*(b + c))', ID="X_1769", classes=["selected", "target"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            central_line(model, X_104, X_106, 104, 106, incident=True)
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_108, X_109, 108, 109, incident=True)
            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)
            return promote_point_to_top(model, X_1769)


        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_1769 on the given reference triangle."""
            model = create_model('X_1769 = MIMOSA TRANSFORM OF X_901')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01769(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-01769.json"))
            write_center_svg(
                model_acute,
                here / "x-01769.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1769¶

X₁₇₆₉¶