← etc / Encyclopedia of Triangle Centers

X₃₁₄₃¶

X₁₁₁-CEVA CONJUGATE OF X₅₂₃

X₃₁₄₃ (X₁₁₁-CEVA CONJUGATE OF X₅₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3143 = X_111-CEVA CONJUGATE OF X_523."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03143(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3143 = X_111-CEVA CONJUGATE OF X_523 on reference triangle ABC."""
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center"])
            X_3143 = ceva_conjugate(model, A, B, C, X_111, X_523, ID="X_3143", 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_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_804 = eval_trilinear_point(model, A, B, C, 'a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))', ID="X_804", classes=["center", "incident"])
            central_line(model, X_115, X_804, 115, 804, incident=True)
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            X_2780 = point_from_barycentrics(model, A, B, C, -0.65368728, -0.09685402, 0.7505413, ID="X_2780", classes=["center", "incident"])
            central_line(model, X_125, X_2780, 125, 2780, incident=True)
            return promote_point_to_top(model, X_3143)


        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_3143 on the given reference triangle."""
            model = create_model('X_3143 = X_111-CEVA CONJUGATE OF X_523')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03143(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-03143.json"))
            write_center_svg(
                model_acute,
                here / "x-03143.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3143¶

X₃₁₄₃¶