← etc / Encyclopedia of Triangle Centers

X₃₁₃₅¶

X₉₆-CEVA CONJUGATE OF X₆

X₃₁₃₅ (X₉₆-CEVA CONJUGATE OF X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3135 = X_96-CEVA CONJUGATE OF X_6."""

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


        def construct_x_03135(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3135 = X_96-CEVA CONJUGATE OF X_6 on reference triangle ABC."""
            X_96 = eval_trilinear_point(model, A, B, C, 'sec(2*A)*sec(B - C)', ID="X_96", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_3135 = ceva_conjugate(model, A, B, C, X_96, X_6, ID="X_3135", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_160 = eval_trilinear_point(model, A, B, C, '(a*((b**(2) + c**(2))*sin(2*A) + (c**(2) - a**(2))*sin(2*B) + (b**(2) - a**(2))*sin(2*C)))', ID="X_160", classes=["center", "incident"])
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            central_line(model, X_160, X_184, 160, 184, incident=True)
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            X_570 = eval_trilinear_point(model, A, B, C, 'sin(A) + sin(2*A)*cos(B - C)', ID="X_570", classes=["center", "incident"])
            central_line(model, X_51, X_570, 51, 570, incident=True)
            return promote_point_to_top(model, X_3135)


        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_3135 on the given reference triangle."""
            model = create_model('X_3135 = X_96-CEVA CONJUGATE OF X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03135(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-03135.json"))
            write_center_svg(
                model_acute,
                here / "x-03135.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3135¶

X₃₁₃₅¶