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X₁₂₀₀¶

3rd SARAGOSSA POINT OF X₅₅

X₁₂₀₀ is the {X₅₅,X₁₁₉₀}-harmonic conjugate of X₄₁. For a list of other harmonic conjugates, click Tables at the top of this page.

X₁₂₀₀ (3rd SARAGOSSA POINT OF X₅₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1200 = 3rd SARAGOSSA POINT OF X_55."""

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


        def construct_x_01200(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1200 = 3rd SARAGOSSA POINT OF X_55 on reference triangle ABC."""
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_1200 = crosspoint(model, A, B, C, X_55, X_57, ID="X_1200", classes=["selected", "target"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            central_line(model, X_41, X_55, 41, 55, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            central_line(model, X_43, X_165, 43, 165, incident=True)
            X_279 = eval_trilinear_point(model, A, B, C, 'csc(A)*(tan(A/2))**(2)', ID="X_279", classes=["center", "incident"])
            central_line(model, X_57, X_279, 57, 279, incident=True)
            return promote_point_to_top(model, X_1200)


        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_1200 on the given reference triangle."""
            model = create_model('X_1200 = 3rd SARAGOSSA POINT OF X_55')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01200(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-01200.json"))
            write_center_svg(
                model_acute,
                here / "x-01200.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1200¶

X₁₂₀₀¶