← etc / Encyclopedia of Triangle Centers

X₆₈₁¶

TRILINEAR POLE OF LINE X₆X_158

X₆₈₁ (TRILINEAR POLE OF LINE X₆X_158) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_681 = TRILINEAR POLE OF LINE X_6X_158."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00681(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_681 = TRILINEAR POLE OF LINE X_6X_158 on reference triangle ABC."""
            X_680 = eval_trilinear_point(model, A, B, C, '((cos(A))**(2)*(sin(B)*(cos(B))**(2) - sin(C)*(cos(C))**(2)))', ID="X_680", classes=["center"])
            X_681 = isogonal_conjugate(model, A, B, C, X_680, ID="X_681", classes=["selected", "target"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_823 = eval_trilinear_point(model, A, B, C, '1/((sec(B))**(2) - (sec(C))**(2))', ID="X_823", classes=["center", "incident"])
            central_line(model, X_110, X_823, 110, 823, incident=True)
            X_1612 = point_from_barycentrics(model, A, B, C, -0.14227031, 0.25578599, 0.88648432, ID="X_1612", classes=["center", "incident"])
            X_1924 = eval_trilinear_point(model, A, B, C, 'a**(4)*(b**(2) - c**(2))', ID="X_1924", classes=["center", "incident"])
            central_line(model, X_1612, X_1924, 1612, 1924, incident=True)
            return promote_point_to_top(model, X_681)


        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_681 on the given reference triangle."""
            model = create_model('X_681 = TRILINEAR POLE OF LINE X_6X_158')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00681(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-00681.json"))
            write_center_svg(
                model_acute,
                here / "x-00681.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X681¶

X₆₈₁¶