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X₃₇₃₈¶

X₂₈₀₄com(HEXYL TRIANGLE)

X₃₇₃₈ = X₅₂₂-of-inner-Garcia triangle

X₃₇₃₈ (X₂₈₀₄com(HEXYL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3738 = X_2804com(HEXYL TRIANGLE)."""

        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,
            feuerbach_point_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03738(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3738 = X_2804com(HEXYL TRIANGLE) on reference triangle ABC."""
            X_2222 = eval_barycentric_point(model, A, B, C, 'a*(a - b)*(a - c)*(a - b + c)*(a + b - c)*(a**(2) - b**(2) + c**(2) - a*c)*(a**(2) - c**(2) + b**(2) - a*b)', ID="X_2222", classes=["center"])
            X_3738 = isogonal_conjugate(model, A, B, C, X_2222, ID="X_3738", classes=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_124 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - a)*(b - c)**(2)*((b + c)*(b**(2) + c**(2) - a**(2) - b*c) + a*b*c))', ID="X_124", classes=["center", "incident"])
            central_line(model, X_11, X_124, 11, 124, incident=True)
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_102, X_104, 102, 104, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_100, X_109, 100, 109, incident=True)
            return promote_point_to_top(model, X_3738)


        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_3738 on the given reference triangle."""
            model = create_model('X_3738 = X_2804com(HEXYL TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03738(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-03738.json"))
            write_center_svg(
                model_acute,
                here / "x-03738.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3738¶

X₃₇₃₈¶