← etc / Encyclopedia of Triangle Centers

X₆₅₇¶

CROSSDIFFERENCE OF X₁ AND X₇

X₆₅₇ = crossdifference of every pair of points on line {1, 7}

X₆₅₇ (CROSSDIFFERENCE OF X₁ AND X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_657 = CROSSDIFFERENCE OF X_1 AND X_7."""

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


        def construct_x_00657(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_657 = CROSSDIFFERENCE OF X_1 AND X_7 on reference triangle ABC."""
            X_657 = eval_trilinear_point(model, A, B, C, '(1 + cos(A))*(cos(B) - cos(C))', ID="X_657", classes=["selected", "target"])
            X_59 = eval_trilinear_point(model, A, B, C, '1/(1 - cos(B - C))', ID="X_59", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_59, X_101, 59, 101, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", 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_9, X_522, 9, 522, incident=True)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_44, X_513, 44, 513, incident=True)
            return promote_point_to_top(model, X_657)


        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_657 on the given reference triangle."""
            model = create_model('X_657 = CROSSDIFFERENCE OF X_1 AND X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00657(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-00657.json"))
            write_center_svg(
                model_acute,
                here / "x-00657.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X657¶

X₆₅₇¶