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X₁₆₅₄¶

1st HATZIPOLAKIS PARALLELIAN POINT

Let P be a point in the plane of, but not on a sideline of, triangle ABC. Let B_A be the point where the line through P parallel to line BC meets line BA, and let C_A be the point where the line through P parallel to line BC meets line CA. Define C_B, A_B, A_C, and B_C cyclically. If P = X₁₆₅₄, then

X₁₆₅₄ (1st HATZIPOLAKIS PARALLELIAN POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1654 = 1st HATZIPOLAKIS PARALLELIAN 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,
            nagel_point_of,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01654(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1654 = 1st HATZIPOLAKIS PARALLELIAN POINT on reference triangle ABC."""
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center"])
            X_1213 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c)*(2*a + b + c))', ID="X_1213", classes=["center"])
            X_1654 = reflection_in_point(model, X_86, X_1213, ID="X_1654", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center", "incident"])
            central_line(model, X_8, X_192, 8, 192, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_319 = eval_trilinear_point(model, A, B, C, '(1 + 2*cos(A))/a**(2)', ID="X_319", classes=["center", "incident"])
            central_line(model, X_37, X_319, 37, 319, incident=True)
            return promote_point_to_top(model, X_1654)


        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_1654 on the given reference triangle."""
            model = create_model('X_1654 = 1st HATZIPOLAKIS PARALLELIAN POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01654(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-01654.json"))
            write_center_svg(
                model_acute,
                here / "x-01654.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1654¶

X₁₆₅₄¶