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X₁₁₄₀¶

INNER PENTAGON POINT

Let A' be the innermost vertex of the regular pentagon erected inward on side BC of ABC. Define B' and C' cyclically. Then triangle A'B'C' is perspective to ABC, and the perspector is X₁₁₄₀. See references at X₁₁₄₀.

X₁₁₄₀ (INNER PENTAGON POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1140 = INNER PENTAGON 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01140(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1140 = INNER PENTAGON POINT on reference triangle ABC."""
            X_1140 = eval_trilinear_point(model, A, B, C, '(csc(A))/(cot(A) - cot(2*pi/5))', ID="X_1140", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1139 = eval_trilinear_point(model, A, B, C, '(csc(A))/(cot(A) + cot(2*pi/5))', ID="X_1139", classes=["center", "incident"])
            central_line(model, X_6, X_1139, 6, 1139, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_3370 = eval_trilinear_point(model, A, B, C, '(sec(A - 2*pi  /5))', ID="X_3370", classes=["center", "incident"])
            central_line(model, X_5, X_3370, 5, 3370, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_3396 = eval_trilinear_point(model, A, B, C, '(sin(A + 2*pi  /5))', ID="X_3396", classes=["center", "incident"])
            central_line(model, X_2, X_3396, 2, 3396, incident=True)
            return promote_point_to_top(model, X_1140)


        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_1140 on the given reference triangle."""
            model = create_model('X_1140 = INNER PENTAGON POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01140(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-01140.json"))
            write_center_svg(
                model_acute,
                here / "x-01140.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1140¶

X₁₁₄₀¶