← etc / Encyclopedia of Triangle Centers

X₈₄₀¶

ISOGONAL CONJUGATE OF X₅₂₈

X₈₄₀ (ISOGONAL CONJUGATE OF X₅₂₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_840 = ISOGONAL CONJUGATE OF X_528."""

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


        def construct_x_00840(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_840 = ISOGONAL CONJUGATE OF X_528 on reference triangle ABC."""
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center"])
            X_518 = eval_trilinear_point(model, A, B, C, '(a*b + a*c - b**(2) - c**(2))', ID="X_518", classes=["center"])
            central_line(model, X_36, X_101, 36, 101)
            central_line(model, X_100, X_518, 100, 518)
            X_840 = intersect_lines(model, X_36, X_101, X_100, X_518, ID="X_840", classes=["selected", "target"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_105, X_513, 105, 513, incident=True)
            return promote_point_to_top(model, X_840)


        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_840 on the given reference triangle."""
            model = create_model('X_840 = ISOGONAL CONJUGATE OF X_528')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00840(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-00840.json"))
            write_center_svg(
                model_acute,
                here / "x-00840.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X840¶

X₈₄₀¶