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X₃₈₂₈¶

X₂₁₀com(4th EULER TRIANGLE)

X₃₈₂₈ = midpoint of X₂ and X₁₀

X₃₈₂₈ (X₂₁₀com(4th EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3828 = X_210com(4th EULER 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            midpoint,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03828(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3828 = X_210com(4th EULER TRIANGLE) on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center"])
            X_3828 = midpoint(model, X_2, X_10, ID="X_3828", classes=["selected", "target"], guide=False)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_121 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - 2*a)*(b**(3) + c**(3) + a*(b**(2) + c**(2)) - 2*b*c*(b + c)))', ID="X_121", classes=["center", "incident"])
            central_line(model, X_115, X_121, 115, 121, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_553 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a + b + c)/(b + c - a)', ID="X_553", classes=["center", "incident"])
            central_line(model, X_12, X_553, 12, 553, incident=True)
            return promote_point_to_top(model, X_3828)


        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_3828 on the given reference triangle."""
            model = create_model('X_3828 = X_210com(4th EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03828(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-03828.json"))
            write_center_svg(
                model_acute,
                here / "x-03828.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3828¶

X₃₈₂₈¶