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X₆₄₈¶

TRILINEAR POLE OF EULER LINE

X₆₄₈ is constructed as the pole of the Euler line L as follows: let A″, B″, C″ be the points where L meets the sidelines BC, CA, AB of ABC. Let A', B', C' be the harmonic conjugates of A″, B″, C″ with respect to {B,C}, {C,A}, {A,B}, respectively, The lines AA', BB', CC' concur in X₆₄₈.

X₆₄₈ (TRILINEAR POLE OF EULER LINE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_648 = TRILINEAR POLE OF EULER LINE."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00648(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_648 = TRILINEAR POLE OF EULER LINE on reference triangle ABC."""
            X_647 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))', ID="X_647", classes=["center"])
            X_648 = isogonal_conjugate(model, A, B, C, X_647, ID="X_648", classes=["selected", "target"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_99, X_112, 99, 112, incident=True)
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_107, X_110, 107, 110, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_264 = eval_trilinear_point(model, A, B, C, 'csc(A)*csc(2*A)', ID="X_264", classes=["center", "incident"])
            central_line(model, X_6, X_264, 6, 264, incident=True)
            return promote_point_to_top(model, X_648)


        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_648 on the given reference triangle."""
            model = create_model('X_648 = TRILINEAR POLE OF EULER LINE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00648(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-00648.json"))
            write_center_svg(
                model_acute,
                here / "x-00648.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X648¶

X₆₄₈¶