← etc / Encyclopedia of Triangle Centers

X₉₄¶

ISOGONAL CONJUGATE OF X₅₀

X₉₄ (ISOGONAL CONJUGATE OF X₅₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_94 = ISOGONAL CONJUGATE OF X_50."""

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


        def construct_x_00094(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_94 = ISOGONAL CONJUGATE OF X_50 on reference triangle ABC."""
            X_50 = eval_trilinear_point(model, A, B, C, 'sin(3*A)', ID="X_50", classes=["center"])
            X_94 = isogonal_conjugate(model, A, B, C, X_50, ID="X_94", classes=["selected", "target"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            X_93 = eval_trilinear_point(model, A, B, C, 'sec(3*A)', ID="X_93", classes=["center", "incident"])
            central_line(model, X_49, X_93, 49, 93, incident=True)
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center", "incident"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            central_line(model, X_23, X_98, 23, 98, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_143 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(2*C - 2*A) + cos(2*A - 2*B))', ID="X_143", classes=["center", "incident"])
            central_line(model, X_4, X_143, 4, 143, incident=True)
            return promote_point_to_top(model, X_94)


        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_94 on the given reference triangle."""
            model = create_model('X_94 = ISOGONAL CONJUGATE OF X_50')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00094(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-00094.json"))
            write_center_svg(
                model_acute,
                here / "x-00094.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X94¶

X₉₄¶