← etc / Encyclopedia of Triangle Centers

X₃₁₇₇¶

X₉-CEVA CONJUGATE OF X₂

X₃₁₇₇ = reflection of X₈₅ in X₁₂₁₂

X₃₁₇₇ (X₉-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_3177 = X_9-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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03177(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3177 = X_9-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center"])
            X_1212 = eval_trilinear_point(model, A, B, C, '(a - b - c)*(b**(2) + c**(2) - a*b - a*c - 2*b*c)', ID="X_1212", classes=["center"])
            X_3177 = reflection_in_point(model, X_85, X_1212, ID="X_3177", 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_85, 2, 85, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_194 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*b**(2) + a**(2)*c**(2) - b**(2)*c**(2))', ID="X_194", classes=["center", "incident"])
            central_line(model, X_63, X_194, 63, 194, incident=True)
            X_144 = eval_trilinear_point(model, A, B, C, '(csc(A))*(tan(B/2) + tan(C/2) - tan(A/2))', ID="X_144", classes=["center", "incident"])
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            central_line(model, X_144, X_145, 144, 145, incident=True)
            return promote_point_to_top(model, X_3177)


        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_3177 on the given reference triangle."""
            model = create_model('X_3177 = X_9-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03177(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-03177.json"))
            write_center_svg(
                model_acute,
                here / "x-03177.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3177¶

X₃₁₇₇¶