← etc / Encyclopedia of Triangle Centers

X₃₅₀₀¶

INTERSECTION OF LINES X₁X_295 AND X₃X_238

X₃₅₀₀ = trilinear pole of line X₆₅₉ X₁₄₅₉

X₃₅₀₀ (INTERSECTION OF LINES X₁X_295 AND X₃X_238) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3500 = INTERSECTION OF LINES X_1X_295 AND X_3X_238."""

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


        def construct_x_03500(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3500 = INTERSECTION OF LINES X_1X_295 AND X_3X_238 on reference triangle ABC."""
            X_3500 = eval_trilinear_point(model, A, B, C, '(1/(a**(2)*b + a**(2)*c - a*(b**(2) + b*c + c**(2)) + b*c*( b + c)))', ID="X_3500", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            central_line(model, X_3, X_238, 3, 238, 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_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_295 = eval_trilinear_point(model, A, B, C, '(cos(A))/(a**(2) - b*c)', ID="X_295", classes=["center", "incident"])
            central_line(model, X_1, X_295, 1, 295, incident=True)
            return promote_point_to_top(model, X_3500)


        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_3500 on the given reference triangle."""
            model = create_model('X_3500 = INTERSECTION OF LINES X_1X_295 AND X_3X_238')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03500(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-03500.json"))
            write_center_svg(
                model_acute,
                here / "x-03500.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3500¶

X₃₅₀₀¶