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X₃₃₅₈¶

MIDPOINT OF X₉ AND X₈₄

X₃₃₅₈ is the midpoint of X₉ and X₈₄.

X₃₃₅₈ (MIDPOINT OF X₉ AND X₈₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3358 = MIDPOINT OF X_9 AND X_84."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            midpoint,
            mittenpunkt_of,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03358(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3358 = MIDPOINT OF X_9 AND X_84 on reference triangle ABC."""
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center"])
            X_84 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C) - cos(A) - 1)', ID="X_84", classes=["center"])
            X_3358 = midpoint(model, X_9, X_84, ID="X_3358", classes=["selected", "target"], guide=False)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_3, X_9, 3, 9, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", 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_11, X_57, 11, 57, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_1445 = point_from_barycentrics(model, A, B, C, 0.10121457, 0.27530364, 0.62348178, ID="X_1445", classes=["center", "incident"])
            central_line(model, X_4, X_1445, 4, 1445, incident=True)
            return promote_point_to_top(model, X_3358)


        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_3358 on the given reference triangle."""
            model = create_model('X_3358 = MIDPOINT OF X_9 AND X_84')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03358(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-03358.json"))
            write_center_svg(
                model_acute,
                here / "x-03358.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3358¶

X₃₃₅₈¶