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X₁₃₂₁¶

1st YIU SQUARES PERSPECTOR

Let \(BB_{A}\)C_AC be the external square on side BC, and define \(CC_{B}\)A_BA and \(AA_{C}\)B_CB cyclically. Let X = BC_B∩CB_C and X' = BA_B∩CA_C, and define Y, Z and Y', Z' cyclically. The lines AX, BY, CZ concur in X₄, and the lines AX', BY', CZ' concur in X₄₈₅. The lines XX', YY', ZZ' concur in X₁₃₂₁, as shown in

X₁₃₂₁ (1st YIU SQUARES PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1321 = 1st YIU SQUARES PERSPECTOR."""

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


        def construct_x_01321(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1321 = 1st YIU SQUARES PERSPECTOR on reference triangle ABC."""
            X_1321 = eval_trilinear_point(model, A, B, C, '((2*cos(A) + sin(A))/((cos(A))**(2) + cos(A)*sin(A)))', ID="X_1321", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_371 = eval_trilinear_point(model, A, B, C, 'cos(A -  pi  /4)', ID="X_371", classes=["center", "incident"])
            central_line(model, X_4, X_371, 4, 371, incident=True)
            X_1322 = eval_trilinear_point(model, A, B, C, '((2*cos(A) - sin(A))/((cos(A))**(2) - cos(A)*sin(A)))', ID="X_1322", classes=["center", "incident"])
            X_2165 = eval_trilinear_point(model, A, B, C, '(sin(A)*sec(2*A))', ID="X_2165", classes=["center", "incident"])
            central_line(model, X_1322, X_2165, 1322, 2165, incident=True)
            return promote_point_to_top(model, X_1321)


        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_1321 on the given reference triangle."""
            model = create_model('X_1321 = 1st YIU SQUARES PERSPECTOR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01321(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-01321.json"))
            write_center_svg(
                model_acute,
                here / "x-01321.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1321¶

X₁₃₂₁¶