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X₁₁₆¶

MIDPOINT OF X₄ AND X₁₀₃

X₁₁₆ is the midpoint of X₄ and X₁₀₃.

X₁₁₆ (MIDPOINT OF X₄ AND X₁₀₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_116 = MIDPOINT OF X_4 AND X_103."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00116(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_116 = MIDPOINT OF X_4 AND X_103 on reference triangle ABC."""
            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=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_2, X_101, 2, 101, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            central_line(model, X_4, X_103, 4, 103, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_118 = point_from_barycentrics(model, A, B, C, 0.28918651, -0.056547619, 0.76736111, ID="X_118", classes=["center", "incident"])
            central_line(model, X_5, X_118, 5, 118, incident=True)
            return promote_point_to_top(model, X_116)


        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_116 on the given reference triangle."""
            model = create_model('X_116 = MIDPOINT OF X_4 AND X_103')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00116(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-00116.json"))
            write_center_svg(
                model_acute,
                here / "x-00116.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X116¶

X₁₁₆¶