← etc / Encyclopedia of Triangle Centers

X₃₄₄₅¶

X₅₆-VERTEX CONJUGATE OF X₅₆

X₃₄₄₅ (X₅₆-VERTEX CONJUGATE OF X₅₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3445 = X_56-VERTEX CONJUGATE OF X_56."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03445(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3445 = X_56-VERTEX CONJUGATE OF X_56 on reference triangle ABC."""
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center"])
            X_3445 = isogonal_conjugate(model, A, B, C, X_145, ID="X_3445", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            central_line(model, X_3, X_106, 3, 106, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_474 = eval_trilinear_point(model, A, B, C, 'cos(A) - (a + b + c)/a', ID="X_474", classes=["center", "incident"])
            central_line(model, X_1, X_474, 1, 474, incident=True)
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            X_999 = eval_trilinear_point(model, A, B, C, '2 - cos(A)', ID="X_999", classes=["center", "incident"])
            central_line(model, X_58, X_999, 58, 999, incident=True)
            return promote_point_to_top(model, X_3445)


        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_3445 on the given reference triangle."""
            model = create_model('X_3445 = X_56-VERTEX CONJUGATE OF X_56')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03445(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-03445.json"))
            write_center_svg(
                model_acute,
                here / "x-03445.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3445¶

X₃₄₄₅¶