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X₃₈₃₀¶

X₃₅₄₃com(EULER TRIANGLE)

X₃₈₃₀ = QA-P24 (AntiComplement of QA-P₁ wrt the Morley Triangle) of quadrangle ABCX₂ (see http://www.chrisvantienhoven.nl/quadrangle-objects/15-mathematics/quadrangle-objects/artikelen-qa/52-qa-p24.html)

X₃₈₃₀ (X₃₅₄₃com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3830 = X_3543com(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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03830(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3830 = X_3543com(EULER TRIANGLE) on reference triangle ABC."""
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center"])
            X_382 = eval_trilinear_point(model, A, B, C, 'cos(A) - 4*cos(B)*cos(C)', ID="X_382", classes=["center"])
            X_3830 = midpoint(model, X_381, X_382, ID="X_3830", 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_265 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*csc(3*A)', ID="X_265", classes=["center", "incident"])
            X_541 = point_from_barycentrics(model, A, B, C, 0.11755139, 0.64096444, -0.75851583, ID="X_541", classes=["center", "incident"])
            central_line(model, X_265, X_541, 265, 541, 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_1384 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) - 5*a**(2))', ID="X_1384", classes=["center", "incident"])
            central_line(model, X_115, X_1384, 115, 1384, incident=True)
            return promote_point_to_top(model, X_3830)


        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_3830 on the given reference triangle."""
            model = create_model('X_3830 = X_3543com(EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03830(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-03830.json"))
            write_center_svg(
                model_acute,
                here / "x-03830.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3830¶

X₃₈₃₀¶