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X₈₆₀¶

INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X₉₂

X₈₆₀ = crossdifference of every pair of points on line X₄₈ X₆₄₇

X₈₆₀ (INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X₉₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_860 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_92."""

        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,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00860(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_860 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_92 on reference triangle ABC."""
            X_860 = eval_trilinear_point(model, A, B, C, '((tan(A) + tan(B))*sin(2*B)*sin(C - A) + (tan(A) + tan(C))*sin(2*C)*sin(B - A))', ID="X_860", 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_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_201 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(B - C))', ID="X_201", classes=["center", "incident"])
            central_line(model, X_10, X_201, 10, 201, incident=True)
            X_240 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(A +  omega  )', ID="X_240", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_240, X_522, 240, 522, incident=True)
            return promote_point_to_top(model, X_860)


        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_860 on the given reference triangle."""
            model = create_model('X_860 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_92')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00860(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-00860.json"))
            write_center_svg(
                model_acute,
                here / "x-00860.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X860¶

X₈₆₀¶