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X₃₈₅₀¶

X₁₄₀com(EULER TRIANGLE)

X₃₈₅₀ = midpoint of X₄ and X₁₄₀

X₃₈₅₀ (X₁₄₀com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3850 = X_140com(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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            midpoint,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03850(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3850 = X_140com(EULER TRIANGLE) on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center"])
            X_3850 = midpoint(model, X_4, X_140, ID="X_3850", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_399 = eval_trilinear_point(model, A, B, C, '5*cos(A) - 4*cos(B)*cos(C) - 8*sin(B)*sin(C)*(cos(A))**(2)', ID="X_399", classes=["center", "incident"])
            X_1199 = point_from_barycentrics(model, A, B, C, 0.23978233, 0.34288074, 0.41733693, ID="X_1199", classes=["center", "incident"])
            central_line(model, X_399, X_1199, 399, 1199, incident=True)
            X_355 = eval_trilinear_point(model, A, B, C, 'a*cos(A) - (b + c)*cos(B - C)', ID="X_355", classes=["center", "incident"])
            X_3633 = eval_trilinear_point(model, A, B, C, 'b*c*(5*a - 2*b - 2*c)', ID="X_3633", classes=["center", "incident"])
            central_line(model, X_355, X_3633, 355, 3633, incident=True)
            return promote_point_to_top(model, X_3850)


        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_3850 on the given reference triangle."""
            model = create_model('X_3850 = X_140com(EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03850(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-03850.json"))
            write_center_svg(
                model_acute,
                here / "x-03850.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3850¶

X₃₈₅₀¶