← etc / Encyclopedia of Triangle Centers

X₂₃₁₃¶

X₂-ISOCONJUGATE OF X₁₂₉₈

X₂₃₁₃ = crosssum of X₁ and X₂₃₁₃

X₂₃₁₃ (X₂-ISOCONJUGATE OF X₁₂₉₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2313 = X_2-ISOCONJUGATE OF X_1298."""

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


        def construct_x_02313(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2313 = X_2-ISOCONJUGATE OF X_1298 on reference triangle ABC."""
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center"])
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center"])
            central_line(model, X_48, X_92, 48, 92)
            central_line(model, X_44, X_513, 44, 513)
            X_2313 = intersect_lines(model, X_48, X_92, X_44, X_513, ID="X_2313", classes=["selected", "target"])
            X_1953 = eval_trilinear_point(model, A, B, C, 'sin(2*B) + sin(2*C)', ID="X_1953", classes=["center", "incident"])
            X_2181 = point_from_barycentrics(model, A, B, C, 0.075264897, 0.15223097, 0.77250413, ID="X_2181", classes=["center", "incident"])
            central_line(model, X_1953, X_2181, 1953, 2181, incident=True)
            return promote_point_to_top(model, X_2313)


        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_2313 on the given reference triangle."""
            model = create_model('X_2313 = X_2-ISOCONJUGATE OF X_1298')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02313(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-02313.json"))
            write_center_svg(
                model_acute,
                here / "x-02313.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2313¶

X₂₃₁₃¶