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X₁₇₈₃¶

MIMOSA TRANSFORM OF X₁₂₆₂

X₁₇₈₃ = trilinear pole of line X₁₉ X₂₅ (the tangent to hyperbola {{A, B, C,X₄,X₁₉}} at X₁₉)

X₁₇₈₃ (MIMOSA TRANSFORM OF X₁₂₆₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1783 = MIMOSA TRANSFORM OF X_1262."""

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


        def construct_x_01783(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1783 = MIMOSA TRANSFORM OF X_1262 on reference triangle ABC."""
            X_905 = eval_trilinear_point(model, A, B, C, '(b - c)*cot(A)', ID="X_905", classes=["center"])
            X_1783 = isogonal_conjugate(model, A, B, C, X_905, ID="X_1783", classes=["selected", "target"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            central_line(model, X_101, X_108, 101, 108, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_100, X_112, 100, 112, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_218 = eval_trilinear_point(model, A, B, C, '((cos(A/2))**(2)*((cos(B/2))**(4) + (cos(C/2))**(4) - (cos(A/2))**(4)))', ID="X_218", classes=["center", "incident"])
            central_line(model, X_4, X_218, 4, 218, incident=True)
            return promote_point_to_top(model, X_1783)


        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_1783 on the given reference triangle."""
            model = create_model('X_1783 = MIMOSA TRANSFORM OF X_1262')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01783(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-01783.json"))
            write_center_svg(
                model_acute,
                here / "x-01783.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1783¶

X₁₇₈₃¶