← etc / Encyclopedia of Triangle Centers

X₃₀₄₈¶

INTERSECTION X₁₁₀X_126∩X₁₁₁X_184

X₃₀₄₈ (INTERSECTION X₁₁₀X_126∩X₁₁₁X_184) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3048 = INTERSECTION X_110X_126∩X_111X_184."""

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


        def construct_x_03048(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3048 = INTERSECTION X_110X_126∩X_111X_184 on reference triangle ABC."""
            X_3048 = eval_trilinear_point(model, A, B, C, '(a**(3)*(a**(4) + b**(4) - c**(4) - 4*a**(2)*b**(2) + 3*b**(2)*c**(2))*(a**(4) - b**(4) + c**(4) - 4*a**(2)*c**(2) + 3*b**(2)*c**(2)))', ID="X_3048", classes=["selected", "target"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_126 = eval_trilinear_point(model, A, B, C, '(b*c*(2*a**(2) - b**(2) - c**(2))*(b**(4) + c**(4) + a**(2)*(b**(2) + c**(2)) - 4*b**(2)*c**(2)))', ID="X_126", classes=["center", "incident"])
            central_line(model, X_110, X_126, 110, 126, incident=True)
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", 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_111, X_184, 111, 184, incident=True)
            X_1147 = eval_trilinear_point(model, A, B, C, '(sin(4*A))/sin(A)', ID="X_1147", classes=["center", "incident"])
            X_1296 = eval_barycentric_point(model, A, B, C, 'a**(2)/((b**(2) - c**(2))*(5*a**(2) - b**(2) - c**(2)))', ID="X_1296", classes=["center", "incident"])
            central_line(model, X_1147, X_1296, 1147, 1296, incident=True)
            return promote_point_to_top(model, X_3048)


        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_3048 on the given reference triangle."""
            model = create_model('X_3048 = INTERSECTION X_110X_126∩X_111X_184')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03048(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-03048.json"))
            write_center_svg(
                model_acute,
                here / "x-03048.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3048¶

X₃₀₄₈¶