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X₁₂₀₈¶

3rd SARAGOSSA POINT OF X₈₄

X₁₂₀₈ (3rd SARAGOSSA POINT OF X₈₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1208 = 3rd SARAGOSSA POINT OF X_84."""

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


        def construct_x_01208(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1208 = 3rd SARAGOSSA POINT OF X_84 on reference triangle ABC."""
            X_84 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C) - cos(A) - 1)', ID="X_84", classes=["center"])
            X_947 = eval_trilinear_point(model, A, B, C, '(a/(a**(3)*(b + c) + (b - c)**(2)*(a**(2) - a*b - a*c - b**(2) - c**(2) - 2*b*c)))', ID="X_947", classes=["center"])
            X_1208 = crosspoint(model, A, B, C, X_84, X_947, ID="X_1208", classes=["selected", "target"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            central_line(model, X_56, X_64, 56, 64, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_963 = eval_trilinear_point(model, A, B, C, 'a/(a**(4) + 2*a**(3)*(b + c) - 4*a**(2)*b*c - (b + c)*(b - c)**(2)*(2*a + b + c))', ID="X_963", classes=["center", "incident"])
            central_line(model, X_6, X_963, 6, 963, incident=True)
            return promote_point_to_top(model, X_1208)


        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_1208 on the given reference triangle."""
            model = create_model('X_1208 = 3rd SARAGOSSA POINT OF X_84')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01208(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-01208.json"))
            write_center_svg(
                model_acute,
                here / "x-01208.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1208¶

X₁₂₀₈¶