← etc / Encyclopedia of Triangle Centers

X₃₁₆₄¶

X₃-CEVA CONJUGATE OF X₂

X₃₁₆₄ = reflection of X₂₆₄ in X₂₁₆

X₃₁₆₄ (X₃-CEVA CONJUGATE OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3164 = X_3-CEVA CONJUGATE OF X_2."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03164(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3164 = X_3-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_264 = eval_trilinear_point(model, A, B, C, 'csc(A)*csc(2*A)', ID="X_264", classes=["center"])
            X_216 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*cos(B - C)', ID="X_216", classes=["center"])
            X_3164 = reflection_in_point(model, X_264, X_216, ID="X_3164", classes=["selected", "target"], guide=False)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_185 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 - cos(A)*cos(B - C))', ID="X_185", classes=["center", "incident"])
            central_line(model, X_20, X_185, 20, 185, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_2, X_216, 2, 216, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_401 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(2*C) - (sin(2*A))**(2))*(csc(A))', ID="X_401", classes=["center", "incident"])
            central_line(model, X_6, X_401, 6, 401, incident=True)
            return promote_point_to_top(model, X_3164)


        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_3164 on the given reference triangle."""
            model = create_model('X_3164 = X_3-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03164(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-03164.json"))
            write_center_svg(
                model_acute,
                here / "x-03164.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3164¶

X₃₁₆₄¶