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X₃₃₂₇¶

INCIRCLE TRANSFORM T(X₂₂₉₀)

X₃₃₂₇ (INCIRCLE TRANSFORM T(X₂₂₉₀)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3327 = INCIRCLE TRANSFORM T(X_2290)."""

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


        def construct_x_03327(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3327 = INCIRCLE TRANSFORM T(X_2290) on reference triangle ABC."""
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center"])
            X_128 = eval_trilinear_point(model, A, B, C, '((sec(A))*(cos(2*B) + cos(2*C))*(1 + 2*cos(2*A))*(cos(2*A) + 2*cos(2*B)*cos(2*C)))', ID="X_128", classes=["center"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center"])
            X_930 = eval_barycentric_point(model, A, B, C, '1/((b**(2) - c**(2))*(a**(4) + b**(4) + c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) - b**(2)*c**(2)))', ID="X_930", classes=["center"])
            central_line(model, X_12, X_128, 12, 128)
            central_line(model, X_55, X_930, 55, 930)
            X_3327 = intersect_lines(model, X_12, X_128, X_55, X_930, ID="X_3327", classes=["selected", "target"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_1141 = eval_trilinear_point(model, A, B, C, 'b*c/(16*D**(2) + (a**(2)+c**(2)-b**(2))*(a**(2)+b**(2)-c**(2)))*(16*D**(2) - 3*(b**(2)+c**(2)-a**(2))**(2))', ID="X_1141", classes=["center", "incident"])
            central_line(model, X_56, X_1141, 56, 1141, incident=True)
            return promote_point_to_top(model, X_3327)


        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_3327 on the given reference triangle."""
            model = create_model('X_3327 = INCIRCLE TRANSFORM T(X_2290)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03327(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-03327.json"))
            write_center_svg(
                model_acute,
                here / "x-03327.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3327¶

X₃₃₂₇¶