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X₃₃₂₂¶

INCIRCLE TRANSFORM T(X₆₆₅)

X₃₃₂₂ = reflection of X₃₃₂₈ in X₁

X₃₃₂₂ (INCIRCLE TRANSFORM T(X₆₆₅)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3322 = INCIRCLE TRANSFORM T(X_665)."""

        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_barycentric_point,
            eval_trilinear_point,
            gergonne_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03322(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3322 = INCIRCLE TRANSFORM T(X_665) on reference triangle ABC."""
            X_3322 = eval_barycentric_point(model, A, B, C, '((2*a**(3) - 2*a**(2)*(b + c) + a*(b**(2) + c**(2)) - (b + c)*(b - c)**(2))**(2)/(b + c - a))', ID="X_3322", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_840 = point_from_barycentrics(model, A, B, C, 0.66666667, -0.32, 0.65333333, ID="X_840", classes=["center", "incident"])
            central_line(model, X_7, X_840, 7, 840, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_1308 = point_from_barycentrics(model, A, B, C, -0.069444444, 0.91666667, 0.15277778, ID="X_1308", classes=["center", "incident"])
            central_line(model, X_56, X_1308, 56, 1308, incident=True)
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            X_1155 = eval_trilinear_point(model, A, B, C, '(cos(B) + cos(C) - 2*cos(A))', ID="X_1155", classes=["center", "incident"])
            central_line(model, X_516, X_1155, 516, 1155, incident=True)
            return promote_point_to_top(model, X_3322)


        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_3322 on the given reference triangle."""
            model = create_model('X_3322 = INCIRCLE TRANSFORM T(X_665)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03322(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-03322.json"))
            write_center_svg(
                model_acute,
                here / "x-03322.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3322¶

X₃₃₂₂¶