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X₃₀₃₄¶

INTERSECTION X₁₀X_116∩X₁₀₅X_386

X₃₀₃₄ = inverse-in-excircles-radical-circle of X₁₁₆

X₃₀₃₄ (INTERSECTION X₁₀X_116∩X₁₀₅X_386) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3034 = INTERSECTION X_10X_116∩X_105X_386."""

        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,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03034(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3034 = INTERSECTION X_10X_116∩X_105X_386 on reference triangle ABC."""
            X_3034 = eval_trilinear_point(model, A, B, C, '(b**(3) - b**(2)*c + b*a**(2) - a*b*c + a**(2)*c - a*c**(2))*(c**(3) - c**(2)*b + c*a**(2) - a*b*c + a**(2)*b - a*b**(2))', ID="X_3034", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_116 = eval_trilinear_point(model, A, B, C, 'b*c*((b - c)**(2)*(b**(2) + b*c + c**(2) - a*b - a*c))', ID="X_116", classes=["center", "incident"])
            central_line(model, X_10, X_116, 10, 116, incident=True)
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            X_386 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_386", classes=["center", "incident"])
            central_line(model, X_105, X_386, 105, 386, incident=True)
            X_528 = point_from_barycentrics(model, A, B, C, -0.26726124, 0.80178373, -0.53452248, ID="X_528", classes=["center", "incident"])
            X_3032 = eval_trilinear_point(model, A, B, C, '(b**(3) + b**(2)*c - b*a**(2) + a*b*c - a**(2)*c - a*c**(2))*(c**(3) + c**(2)*b - c*a**(2) + a*b*c - a**(2)*b - a*b**(2))', ID="X_3032", classes=["center", "incident"])
            central_line(model, X_528, X_3032, 528, 3032, incident=True)
            return promote_point_to_top(model, X_3034)


        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_3034 on the given reference triangle."""
            model = create_model('X_3034 = INTERSECTION X_10X_116∩X_105X_386')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03034(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-03034.json"))
            write_center_svg(
                model_acute,
                here / "x-03034.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3034¶

X₃₀₃₄¶