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X₃₃₂₃¶

INCIRCLE TRANSFORM T(X₆₉₂)

X₃₃₂₃ = trilinear pole wrt intouch triangle of line X₆ X₇

X₃₃₂₃ (INCIRCLE TRANSFORM T(X₆₉₂)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3323 = INCIRCLE TRANSFORM T(X_692)."""

        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_03323(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3323 = INCIRCLE TRANSFORM T(X_692) on reference triangle ABC."""
            X_3323 = eval_barycentric_point(model, A, B, C, '((b - c)**(2)*(b**(2) + c**(2) - a*b - a*c)**(2)/(b + c - a))', ID="X_3323", 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_348 = eval_trilinear_point(model, A, B, C, 'cot(A)*(sec(A/2))**(2)', ID="X_348", classes=["center", "incident"])
            X_1083 = eval_trilinear_point(model, A, B, C, 'a**(4) - a**(3)*(b + c) - a**(2)*b*c + 2*a*b*c*(b + c) - b*c*(b**(2) + c**(2))', ID="X_1083", classes=["center", "incident"])
            central_line(model, X_348, X_1083, 348, 1083, incident=True)
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            X_1358 = eval_trilinear_point(model, A, B, C, '(tan(A/2))**(2)*(sin(B/2 - C/2))**(2)', ID="X_1358", classes=["center", "incident"])
            central_line(model, X_514, X_1358, 514, 1358, incident=True)
            return promote_point_to_top(model, X_3323)


        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_3323 on the given reference triangle."""
            model = create_model('X_3323 = INCIRCLE TRANSFORM T(X_692)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03323(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-03323.json"))
            write_center_svg(
                model_acute,
                here / "x-03323.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3323¶

X₃₃₂₃¶