← etc / Encyclopedia of Triangle Centers

X₂₈₂¶

X₆-CROSS CONJUGATE OF X₉

X₂₈₂ (X₆-CROSS CONJUGATE OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_282 = X_6-CROSS CONJUGATE OF X_9."""

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


        def construct_x_00282(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_282 = X_6-CROSS CONJUGATE OF X_9 on reference triangle ABC."""
            X_223 = eval_trilinear_point(model, A, B, C, '(tan(A/2))*(cos(B) + cos(C) - cos(A) - 1)', ID="X_223", classes=["center"])
            X_282 = isogonal_conjugate(model, A, B, C, X_223, ID="X_282", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            central_line(model, X_3, X_9, 3, 9, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            central_line(model, X_2, X_77, 2, 77, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center", "incident"])
            central_line(model, X_19, X_102, 19, 102, incident=True)
            return promote_point_to_top(model, X_282)


        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_282 on the given reference triangle."""
            model = create_model('X_282 = X_6-CROSS CONJUGATE OF X_9')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00282(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-00282.json"))
            write_center_svg(
                model_acute,
                here / "x-00282.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X282¶

X₂₈₂¶