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X₁₁₁₉¶

2nd HATZIPOLAKIS PERSPECTOR

Let triangle A₀B₀C₀ be as defined for X₁₁₁₈. Let A₁ be the orthogonal projection of A₀ onto line BC, and define B₁ and C₁ cyclically. Then triangle A₁B₁C₁ is perspective to ABC, and the perspector is X₁₁₁₉. (Antreas Hatzipolakis, #5321, 4/30/02)

X₁₁₁₉ (2nd HATZIPOLAKIS PERSPECTOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1119 = 2nd HATZIPOLAKIS PERSPECTOR."""

        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,
            gergonne_point_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01119(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1119 = 2nd HATZIPOLAKIS PERSPECTOR on reference triangle ABC."""
            X_1119 = eval_trilinear_point(model, A, B, C, '((1 - sec(A))/(1 + cos(A)))', ID="X_1119", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_4, X_7, 4, 7, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_19, X_57, 19, 57, incident=True)
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            X_269 = eval_trilinear_point(model, A, B, C, '(tan(A/2))**(2)', ID="X_269", classes=["center", "incident"])
            central_line(model, X_34, X_269, 34, 269, incident=True)
            return promote_point_to_top(model, X_1119)


        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_1119 on the given reference triangle."""
            model = create_model('X_1119 = 2nd HATZIPOLAKIS PERSPECTOR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01119(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-01119.json"))
            write_center_svg(
                model_acute,
                here / "x-01119.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1119¶

X₁₁₁₉¶