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X₃₇₅₁¶

X₁₇₂₁com[INVERSE(n(HEXYL TRIANGLE))]

Let A'B'C' denote the inverse of the normalized hexyl triangle. Then A', expressed in homogeneous barycentrics (i.e., not normalized), is given by

X₃₇₅₁ (X₁₇₂₁com[INVERSE(n(HEXYL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3751 = X_1721com[INVERSE(n(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_trilinear_point,
            incenter_of,
            promote_point_to_top,
            reflection_in_point,
            spieker_center_of,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03751(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3751 = X_1721com[INVERSE(n(HEXYL TRIANGLE))] on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_3751 = reflection_in_point(model, X_1, X_6, ID="X_3751", classes=["selected", "target"], guide=False)
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_10, X_69, 10, 69, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_43, X_57, 43, 57, incident=True)
            return promote_point_to_top(model, X_3751)


        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_3751 on the given reference triangle."""
            model = create_model('X_3751 = X_1721com[INVERSE(n(HEXYL TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03751(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-03751.json"))
            write_center_svg(
                model_acute,
                here / "x-03751.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3751¶

X₃₇₅₁¶