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X₃₆₂¶

CONGRUENT CIRCUMCIRCLES ISOSCELIZER POINT

The isoscelizer equations u(X)/a = v(X)/b = w(X)/c have solution X = X₃₆₂.

X₃₆₂ (CONGRUENT CIRCUMCIRCLES ISOSCELIZER POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_362 = CONGRUENT CIRCUMCIRCLES ISOSCELIZER POINT."""

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


        def construct_x_00362(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_362 = CONGRUENT CIRCUMCIRCLES ISOSCELIZER POINT on reference triangle ABC."""
            X_362 = eval_trilinear_point(model, A, B, C, 'b*cos(B/2) + c*cos(C/2) - a*cos(A/2)', ID="X_362", classes=["selected", "target"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_234 = eval_trilinear_point(model, A, B, C, '((cos(B/2) + cos(C/2))*(cos(B/2)*cos(C/2))**(2))', ID="X_234", classes=["center", "incident"])
            central_line(model, X_57, X_234, 57, 234, incident=True)
            return promote_point_to_top(model, X_362)


        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_362 on the given reference triangle."""
            model = create_model('X_362 = CONGRUENT CIRCUMCIRCLES ISOSCELIZER POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00362(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-00362.json"))
            write_center_svg(
                model_acute,
                here / "x-00362.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X362¶

X₃₆₂¶