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X₁₃₃₁¶

ORTHOCORRESPONDENT OF X₁₀₁

For the definition of orthocorrespondent, see the notes just before X₁₉₉₂.

X₁₃₃₁ (ORTHOCORRESPONDENT OF X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1331 = ORTHOCORRESPONDENT OF X_101."""

        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_01331(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1331 = ORTHOCORRESPONDENT OF X_101 on reference triangle ABC."""
            X_1331 = eval_trilinear_point(model, A, B, C, '(cos(A))/(b - c)', ID="X_1331", classes=["selected", "target"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_100, X_109, 100, 109, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_101, X_110, 101, 110, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_212 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(A))', ID="X_212", classes=["center", "incident"])
            central_line(model, X_63, X_212, 63, 212, incident=True)
            return promote_point_to_top(model, X_1331)


        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_1331 on the given reference triangle."""
            model = create_model('X_1331 = ORTHOCORRESPONDENT OF X_101')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01331(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-01331.json"))
            write_center_svg(
                model_acute,
                here / "x-01331.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1331¶

X₁₃₃₁¶