← etc / Encyclopedia of Triangle Centers

X₃₄₉₈¶

INTERSECTION OF LINES X₃X_83 AND X₁₉₄X_263

X₃₄₉₈ (INTERSECTION OF LINES X₃X_83 AND X₁₉₄X_263) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3498 = INTERSECTION OF LINES X_3X_83 AND X_194X_263."""

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


        def construct_x_03498(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3498 = INTERSECTION OF LINES X_3X_83 AND X_194X_263 on reference triangle ABC."""
            X_3498 = eval_trilinear_point(model, A, B, C, '(b*c*(2*a**(6)*(b**(2) + c**(2)) + a**(4)*(b**(4) + 3*b**(2)*c**(2) + c**(4)) + a**(2)*b**(2)*c**(2)*(b**(2) + c**(2)) + b**(4)*c**(4))/(a**(4) - a**(2)*b**(2) - a**(2)*c**(2) - 2*b**(2)*c**(2)))', ID="X_3498", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_83 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) + c**(2))', ID="X_83", classes=["center", "incident"])
            central_line(model, X_3, X_83, 3, 83, incident=True)
            X_3495 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b**(2)*c**(2) + c**(2)*a**(2) + a**(2)*b**(2) - a*b*c*(b + c - a)))', ID="X_3495", classes=["center", "incident"])
            X_3501 = eval_trilinear_point(model, A, B, C, '(a - b)*(a - c)*(b + c) + a*b*c', ID="X_3501", classes=["center", "incident"])
            central_line(model, X_3495, X_3501, 3495, 3501, incident=True)
            return promote_point_to_top(model, X_3498)


        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_3498 on the given reference triangle."""
            model = create_model('X_3498 = INTERSECTION OF LINES X_3X_83 AND X_194X_263')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03498(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-03498.json"))
            write_center_svg(
                model_acute,
                here / "x-03498.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3498¶

X₃₄₉₈¶