← etc / Encyclopedia of Triangle Centers

X₁₁₂₈¶

2nd DE VILLIERS POINT

X₁₁₂₈ (2nd DE VILLIERS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1128 = 2nd DE VILLIERS POINT."""

        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_01128(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1128 = 2nd DE VILLIERS POINT on reference triangle ABC."""
            X_1128 = eval_trilinear_point(model, A, B, C, '((sin(( pi  - A)/4))/sin(( pi  + 3*A)/4))', ID="X_1128", classes=["selected", "target"])
            X_164 = eval_trilinear_point(model, A, B, C, 'sin(B/2) + sin(C/2) - sin(A/2)', ID="X_164", classes=["center", "incident"])
            X_173 = eval_trilinear_point(model, A, B, C, 'cos(B/2) + cos(C/2) - cos(A/2)', ID="X_173", classes=["center", "incident"])
            central_line(model, X_164, X_173, 164, 173, incident=True)
            X_188 = eval_trilinear_point(model, A, B, C, 'csc(A/2)', ID="X_188", classes=["center", "incident"])
            X_519 = eval_trilinear_point(model, A, B, C, '(2*a - b - c)/a', ID="X_519", classes=["center", "incident"])
            central_line(model, X_188, X_519, 188, 519, incident=True)
            X_258 = eval_trilinear_point(model, A, B, C, '1/(cos(B/2) + cos(C/2) - cos(A/2))', ID="X_258", classes=["center", "incident"])
            X_505 = eval_trilinear_point(model, A, B, C, '(1/(sin(B/2) + sin(C/2) - sin(A/2)))', ID="X_505", classes=["center", "incident"])
            central_line(model, X_258, X_505, 258, 505, incident=True)
            return promote_point_to_top(model, X_1128)


        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_1128 on the given reference triangle."""
            model = create_model('X_1128 = 2nd DE VILLIERS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01128(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-01128.json"))
            write_center_svg(
                model_acute,
                here / "x-01128.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1128¶

X₁₁₂₈¶