← etc / Encyclopedia of Triangle Centers

X₈₅₇¶

INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X₇₅

X₈₅₇ = inverse-in-orthocentroidal-circle of X₃₇₉

X₈₅₇ (INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X₇₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_857 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_75."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00857(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_857 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_75 on reference triangle ABC."""
            X_857 = eval_trilinear_point(model, A, B, C, '((sin(C))**(2)*sin(2*B)*sin(C - A) + (sin(B))**(2)*sin(2*C)*sin(B - A))', ID="X_857", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center", "incident"])
            central_line(model, X_514, X_661, 514, 661, incident=True)
            return promote_point_to_top(model, X_857)


        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_857 on the given reference triangle."""
            model = create_model('X_857 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_75')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00857(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-00857.json"))
            write_center_svg(
                model_acute,
                here / "x-00857.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X857¶

X₈₅₇¶