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X₁₆₅₅¶

2nd HATZIPOLAKIS PARALLELIAN POINT

Continuing from the description of X₁₆₅₄, let h(B,A) be the distance from the point B_A to the line CA, and define five other distances cyclically. If P = X₁₆₅₅, then

X₁₆₅₅ (2nd HATZIPOLAKIS PARALLELIAN POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1655 = 2nd 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 (
            anticomplement,
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01655(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1655 = 2nd HATZIPOLAKIS PARALLELIAN POINT on reference triangle ABC."""
            X_274 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c)', ID="X_274", classes=["center"])
            X_1655 = anticomplement(model, A, B, C, X_274, ID="X_1655", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, 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_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_385 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - b**(2)*c**(2))', ID="X_385", classes=["center", "incident"])
            central_line(model, X_21, X_385, 21, 385, incident=True)
            return promote_point_to_top(model, X_1655)


        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_1655 on the given reference triangle."""
            model = create_model('X_1655 = 2nd HATZIPOLAKIS PARALLELIAN POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01655(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-01655.json"))
            write_center_svg(
                model_acute,
                here / "x-01655.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1655¶

X₁₆₅₅¶