← etc / Encyclopedia of Triangle Centers

X₁₉₄¶

X₆-CEVA CONJUGATE OF X₂

X₁₉₄ = reflection of X₇₆ in X₃₉

X₁₉₄ (X₆-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_194 = X_6-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,
            incenter_of,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00194(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_194 = X_6-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center"])
            X_194 = reflection_in_point(model, X_76, X_39, ID="X_194", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_87 = eval_trilinear_point(model, A, B, C, '1/(a*b + a*c - b*c)', ID="X_87", classes=["center", "incident"])
            central_line(model, X_1, X_87, 1, 87, incident=True)
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_32, X_99, 32, 99, incident=True)
            return promote_point_to_top(model, X_194)


        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_194 on the given reference triangle."""
            model = create_model('X_194 = X_6-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00194(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-00194.json"))
            write_center_svg(
                model_acute,
                here / "x-00194.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X194¶

X₁₉₄¶