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X₃₂₄₆¶

MIDPOINT OF X₁ AND X₄₄

X₃₂₄₆ is the midpoint of X₁ and X₄₄.

X₃₂₄₆ (MIDPOINT OF X₁ AND X₄₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3246 = MIDPOINT OF X_1 AND X_44."""

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


        def construct_x_03246(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3246 = MIDPOINT OF X_1 AND X_44 on reference triangle ABC."""
            X_3246 = eval_trilinear_point(model, A, B, C, '4*a**(2) + b**(2) + c**(2) - 4*b*c - c*a - a*b', ID="X_3246", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_88 = eval_trilinear_point(model, A, B, C, '1/(b + c - 2*a)', ID="X_88", classes=["center", "incident"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            central_line(model, X_88, X_105, 88, 105, incident=True)
            X_678 = eval_trilinear_point(model, A, B, C, '((b + c - 2*a)**(2))', ID="X_678", classes=["center", "incident"])
            X_899 = eval_trilinear_point(model, A, B, C, '1/b + 1/c - 2/a', ID="X_899", classes=["center", "incident"])
            central_line(model, X_678, X_899, 678, 899, incident=True)
            return promote_point_to_top(model, X_3246)


        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_3246 on the given reference triangle."""
            model = create_model('X_3246 = MIDPOINT OF X_1 AND X_44')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03246(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-03246.json"))
            write_center_svg(
                model_acute,
                here / "x-03246.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3246¶

X₃₂₄₆¶