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X₁₅₆₂¶

ORTHOJOIN OF X₅₂₀

X₁₅₆₂ (ORTHOJOIN OF X₅₂₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1562 = ORTHOJOIN OF X_520."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01562(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1562 = ORTHOJOIN OF X_520 on reference triangle ABC."""
            X_393 = eval_trilinear_point(model, A, B, C, 'b*c*(tan(A))**(2)', ID="X_393", classes=["center"])
            X_647 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))', ID="X_647", classes=["center"])
            X_1562 = ceva_conjugate(model, A, B, C, X_393, X_647, ID="X_1562", classes=["selected", "target"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_115, X_125, 115, 125, incident=True)
            X_148 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - (b**(2) - c**(2))**(2) + b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_148", classes=["center", "incident"])
            X_287 = eval_trilinear_point(model, A, B, C, 'cot(A)*sec(A +  omega  )', ID="X_287", classes=["center", "incident"])
            central_line(model, X_148, X_287, 148, 287, incident=True)
            X_127 = eval_trilinear_point(model, A, B, C, 'b*c*(sin(2*B) - sin(2*C))*((b**(2) - c**(2))*sin(2*A) - b**(2)*sin(2*B) + c**(2)*sin(2*C))', ID="X_127", classes=["center", "incident"])
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center", "incident"])
            central_line(model, X_127, X_525, 127, 525, incident=True)
            return promote_point_to_top(model, X_1562)


        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_1562 on the given reference triangle."""
            model = create_model('X_1562 = ORTHOJOIN OF X_520')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01562(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-01562.json"))
            write_center_svg(
                model_acute,
                here / "x-01562.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1562¶

X₁₅₆₂¶