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X₃₂₅₃¶

INTERSECTION OF X₆X_190 AND X₂₃₈X_874

X₃₂₅₃ (INTERSECTION OF X₆X_190 AND X₂₃₈X_874) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3253 = INTERSECTION OF X_6X_190 AND X_238X_874."""

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


        def construct_x_03253(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3253 = INTERSECTION OF X_6X_190 AND X_238X_874 on reference triangle ABC."""
            X_3253 = eval_trilinear_point(model, A, B, C, '(b*c*(a**(2) - b*c)/(b**(2)*c - b**(2)*a + c**(2)*b - c**(2)*a))', ID="X_3253", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            central_line(model, X_6, X_190, 6, 190, incident=True)
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            X_874 = point_from_barycentrics(model, A, B, C, 4.4210526, 0.10835913, -3.5294118, ID="X_874", classes=["center", "incident"])
            central_line(model, X_238, X_874, 238, 874, incident=True)
            X_727 = eval_trilinear_point(model, A, B, C, '(1/(a **(-3)*(b **(-1) + c **(-1)) - a **(-2)*(b **(-2) + c **(-2))))', ID="X_727", classes=["center", "incident"])
            X_789 = eval_trilinear_point(model, A, B, C, 'a **(- 2)/(b**(3) - c**(3))', ID="X_789", classes=["center", "incident"])
            central_line(model, X_727, X_789, 727, 789, incident=True)
            return promote_point_to_top(model, X_3253)


        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_3253 on the given reference triangle."""
            model = create_model('X_3253 = INTERSECTION OF X_6X_190 AND X_238X_874')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03253(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-03253.json"))
            write_center_svg(
                model_acute,
                here / "x-03253.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3253¶

X₃₂₅₃¶